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OF 





HDITl'D BY 

SIR RICHARD GLAZEBR.OOK 

K.C.U., D.Sc., F.R.S. 



IN FIVE VOLUMES 

VOL. I 
MECHANICS-ENGINEE1UNG-HEAT 



MACMILLAN AND CO., LIMITED 

ST. MARTIN'S STREET, LONDON 

1922 



COPYRIGHT 



PRINTED IN GREAT 1JRITAIN 



PEEFACE 






ivo workers to whoso efforts thoy arc due. 

To M out what are tho latent niothoclB of Oalorimotry, whul exactly^ 
,wn aboutiho law, of Friction, how far ha, Iho theory of llu, Htomn J^ino 
mncod, what are tho principle* on which mcilhoila of aceiimlo g-uigiiifi 01 n 
, dote nmnation of tho numy factor, which conio into tho luy-oul of a l h 
ct ^ It he design of a Dynamo, or llLon.otliodH.of Pyromctry ,tro based, 
nn" a lontj BO-ireli in Libraries and, nob infroqnoiitly, a futile jmirnoy t.. tmmo 
ic" whoro'it ii liopo.1 tho wiHliocl-fov information may ho found 

The Scionco of Aor.n.utic., tho Doeigii of Optical IiiHtnimo ntB, 1 W McU o,ta 
Metallurgy, tho Construction of ClorM TeloB C opo or MwroacopOH, thu J.IWH 
Mimip and Acoustics uro all baaed on Physics. 

T ,lL,r who U co,,ce,,ed with .hone ,,,1, indeed, w,t , ,,,uu tta. 
l,or B nl)ioets nu, a t know, not perhaps all that lin boon dono-that would bo 
u heavy a task-but where ho may find tho latnt and most to .nfonna- 

m ::^:;t:;:^^ 

qy rsir?^^"^-- - ~ ^^'-\ 

1 h , BOO , from L nanJel of so.no of Iho principal eontdbnUms tt.o M-tor h,. 
", L ato h, wiring tho help of those ,uot con.po.ont to wnto ,m tub 

tluu 

r 1 h< the Dictionary could not havo been produced Ho a IHO , o t ,1 
, H ,,nb r of Sclcntlfl. fk-doto ^l.oHO Cou,,oi. S have allowod uo ,,f ., ,v 
U1H -from theiv 7Vi/ to be froely ,nalo. Among ll 'l' , '"'. "'" 
ionert in particular tho Koyal Socioty, tho Institution of Mlm,,..nl l.nco. 



YX PKEFACE 



and the Institution of Electrical Engineers. The same help has bcoti raulily 
itllbrdcd by it number of Pub] labors. 

It la clear that, with so largo ;i range of subjects, any individual worker will, 
probably, bo concerned mainly with 0110 branch, ami, with tliis in viinv, tlic 
volumes have been aminged, us far as jinsaiblc, in snbjocts. To obtjiin informa- 
tion as to the latest advances of Applied Electricity it will not bo noeossuvy to 
purcliaso the aections of the Dictionary dealing witli Aorouantins or Mutcsorology, 
Tiio iirrangcuicnt in ouch volume is alphabetical, but, at the saimi time, it lias 
been thought best to deal with each main subject for example, the Thevmo- 
(.lyuamies of the Steam Engine in a continuous article ; references are given, 
each in its own alphabetical position, to the headings of tho various fictitious of 
ui\ article and to the more important subjects which it includes, 

U* T (' 
Xiv 1 . l;r, 



LIST 01? CONTRIBUTORS 

MECHANICS AND ENGI!MKEKINC! 



n A ir p HI Iu9t.C.K, MJ.Meoh.3S. 
BATSOS, KTSUTSAI.P 0., A.K.G., AI..IUSI. 

]3|, w tic Constant*, Dctornnnntion ol. 



EVASB, Aumnav T., O.B-E, H.I.A.K . 
Poti-ol Ifingine, Tim 



Hydmulica. 

J. H., A.M.Imt.C.15., 
Dynamometers. - 
Mechanical Power*. 



Pressure, Measurement ot. 
^ Hoiuwro, SC.D, 1?.B,S. - 

'JToiU'icr's Scries. 
'i .Simple Harmonic Motion. 

Stroam-Uno Motion. 

T,AHDON, J. W., M.A. . 

Structures, Strength of. 



Kincinntics of 

GRUIOKSIIANK, AHIWB 

SlA^aiu TSngiM, Iteciin-oculiiiB. . 

i? r; ^ M tnfit,O.K, M.I.McchJ'1, A.M.l.N-A. 

DAH*Y,WaHAllKBWKOT,l.W.fo.,M.LlBl,U , 

Enine ail Prime Movers Uii^ of- 
DOWSON, 



vu 



VIU 



LIST OTf CONTRIBUTORS 



LEVY, HYMAN, M.A., D.SO., F.11.S.E. lu \'' 

Dynamical Similarity. 
UBHKAHCH STAKF, GENERAL ELECTRIC Co. , . - u - K - 

Air-pumps. 

SOUTHWELL, II. V., M.A. . 

Elasticity, Theory of. 
STAHTOH, T. IS, 0.13.13., US,,, Hl.ln B t,O.K, KH.S 

li'iicUon. 

STONED QKBALD, D.Sc., M.Insl,C..IC, KH.H., and 
PUTRIK, TRLVOHD, "AI.Sc, 

Steam Turbine, Physics of thu. 



BwTi'iinFiKM), W. J. A., M.A., V.I.O. . 

Fuel Calorimetry. 

CJ.TSIUI, Sir DuaAMi, M.tn*t.O.E., M.I.Mech.E., 17.H.S., awl ) - 
BURLS, tl. A., M.lust.C.K, M.Inst.A.E. J 

Engines, ThurmoilyimmicB of Internal Ciimlmslion. 

Engines, Some Typical Internal Combustion. 

DAY, ARTHUR L., I'h.D-, Se -' D '' aild SOHMAH, HOIIERT B., Ph.D.,| . . A. i, 

Gcopliysk-al Institute, Washington, U.S.A. J ll - 

Temperature, UeaJiaation of Absolute, Scalu of. 
UWINCI, Sir JAMES AI.PIIBI), K.C.B., 1,1,1)., I'MiS ^. A . 

Liquefaction of Gases. 

Refrigeration. 

Steam Engine, Theory of, 

Tliennotly nan tics. 

TS, ERNEST HOWARD, Sc.D., LL.])., V.R&. . '' ; - ll - 

Heat, Jleohaiiical li(juivale]it of, 

.8, EZBH, D.Sc. .....' ri 

Bomb Calorimeters. 

Calorimetry, Electrical Methods. 

Calorimelry, Method of Mixtures. 

Caloilmetry, Methods liaswl on Ohangu oE State,. 

Calorinnitry, Quantum Theory, 

Latent Heat. 

Pyrometry, Optical. 

Tyrometry, Total Radiation. 

Hoaistaii co Thermometers. 

Thcraiocouplca. 



LIST Off CONTRIBUTORS 

1-lALlOY, WlLT.fAM 11 ATM, JLA., I'Ml.H. - 

i, JOHN L., 1>.M(!., KIiiBt.l J . . 




LAM it, lloitACK, S-M-.O., I'Ml.S. . 

Jouduiaion ol' : ,MaUimiuit.ii:al Tln:ory. 



KU \VTM.IAJI, ILMf-., K.K.S, 
\|uiHi(m. 

I'VK, DAVID K., SLA. ... 
GHHUH, Sptioifm ]To,'U; ol 1 . 

Honoii'iHi.iJ, K II., .H.A., H.H(5. 

1 1 ciil, Conduction ol'. 
lldtvt,, OunvuuliiiH of. 



DICTIONARY O.P APPLIED PHYSICS 



ABSOLUTE SOALI'l OK TJ3M1'J311AT01U5 AIE METERS 



A 



AllSULUTH FJOAIJH OF TBHI'HHATUHK_(Kl)lvill). 

J[ a pir[i!i;tly rovorsiblu hnat ciHiinn UUUJB 
in iv quantity of hunt Qi a^tompuratum T, 
and rojootH Q a at timipiii'atum T a , tlmn 
(). l l'K l - Q a /l'a provided tins tmniii'iutiireH 
T, and T a am moamired on Hid alwuhitK 
tluii'iiiiidyiiainio Botilit. llcm^ thn ratio 
of two limi|imiturcH on tliat Hdaln is i!(|tial 
to tliti ratio of Lliu lu-nt lakuii In to th 
Jiout mjuutuil by any porfticlly rovm-^blo 
ongiuo working bolwcou tlioao tmnpnraiiun^. 
Sou " TliormodyiiainitiH," 88 ( 17 )' ( 2 -) ' 
" .Kiitdnoii, 'I'liKnnodynainiiiH of .InLninal 

AlWlH^UTH HBUO.'.UKFINITinHH III', <'N "_ C)AH " 
AND "WOIIK" HUAliKH. HlIU 

dymuniuH," ('t). 
AHHUKPTION DYNAMOMBTEKS. Kco 

DHitCI'H," (2). 

AnHoui'TioN OF RADIATION AH 

Tlll'l Kl-JAIHNH )!.' 

BIKTBR8. Hoc " Pyromutry, Total 
Uon,"(]0). 



L'UMi'S. Sets " Air - 



- 
An no DYNAMIC TACiiKOMETiiR : ' Jni' measuring 

ninnlior of nivolntitiiiH iitu 1 unit timo by 
iiH'aiiH of nir iirosauro ilifforoncos. Suo 
" Mutora," 5 01), Vol. TIT. 
AKUU--KNUINI.;, Tun llor^s-KiiYon " EAGLE." 
Kiso " Potrol HiiKiiw, 'J-)c Wator-coiiLod," 



Movalilo. Hno ibid, (!)). 
Ati(!i3i,iiiiATioN IMAIIHH. Kco 

of iVachmovy," (4)(iv.). 
At](JiiMUf.A'i'oitfi,HYmtAiir,i(i. hco 



. 

AIJIAIIATIO CiiAiron. A n\\tmw ]n tl10 
aiul iiroBBuru of a body otM'Hwl out 
ibly i siiuli a way that no hunt ia allowod 
to pafin to or from tho body. Sue aim 
" Tliormoilynaniios," (JO), (118). 

ADIAIUTIO EQUATION FOR A PiwraiT CTAH. 
j Sco " EnginoH, Tlint-motlynnniioH of 
Comliiiutinn," (20); 



,, 

EXI'AKSUIN 0V A .In.UlI). 



-- , v 

AHUOHTATIO I-'UMTH, TICEORY OK hoc Air- 
piinipH," g (S). 

Allt, (JUNHTITIIKNTH Of, SKrAKATHI) 1IY IntAO- 
TfONAF, :i)WTILLATI()N. Suo " GaSOS, LlllUO- 

faction of," (ii). 

Aiu, JNDKX OF HuniAtiriON m', uscwl as 

HitiMindnry Hfcnndiu'd tomiionitiiro in tko 

itinu ftlicivo IH)U (J. Hco " Tompomturo, 

KtnUiHatioii of Alwolutu Sualii of," 0>1) ( ll -)- 

Am, KfKUiKict JlMATov: 

At liigli U'iniwrotwro. Ron "OasM, bjicoiUo 

Iloalof, at JMKhToiniwratiiPOH. 11 - 

At 00 fJ. mid various prcmnwH, tabiilotwi 

vftluoa (il)tainod by Holliorn and Jacob. 

fioo " CliUorimoU-y, 3'Mcotricat Mcthotla of, 

(10), TnWoX. 
Variation wltli prcHdiiro over tho rango 

1 to 1200 nlmoaiilioroH, cldtornunod by 

Jlolljom and Jnooli. Sco i&W. (US). 

Alii (HBB FKOM CO,), Bl'KCIIfia IlWATfl OBt 

tobulatwl vniiicB obliaincd by Sohcol nnd 
IloiiKO. Son " Oalorimotry, Jl-loctnoal 




(38). 

AH!) THOTIimiMAL (JltANUKS. K(H1 

, TlioimodyiiaiiiiiiH nf Tntuniiil 
(3) J 



l . 

Am AND o'l'uim OAHKH, HPMJIFIO HMAT 01, 
(lotorminoil at mom and liiw toniporuturw 
bv tho cnntinmiuR How oloofcnun molhoil, 
]y ftcthool and Honso. Soo lt Cnlcirunotiy, 
lamiti'iwil Methods of," (IT)). 

Am AND HTKAM MBTMWS, OAumiA'TioN or. 
Soo " Motors fin aimiHiiromont of Stoani, 
<r>) t Vol. HI. 

Allt- UOMl'ItlMH ION KlJFUiaKllATINO 

Hwi " HiiEriKBratlon," (4). 
Atn-Lirp 1'usiP. Hwi " irydranlicii,' IT. 5 I' 1 ")- 
Am MBTKUS. Sno "C ( ftl-B8 Wl Air 

vi. nr. 



AIR-PUMPS 



AIR-PUMPS 
INTRODUCTION 

S (]} COMPRESSORS, KVAOUATOBH, HLOWRHB. 
An air- or gna-iiurap IB a device whereby gas 
la transfm-red from a low - prMSiiw vcMol 
(LP.V.) to a high-pressure vessel (11.1. V.)- 
The term " vessel " includes tho froo atmo- 
Hphoro, and tho term " gas " includes vapours. 
It is assumed, unless tho contrary is stated, 
that the L.P.V. and H.P.V. are at tho BAIUO 
temperature. 

If the L.P.V. mid H.P.V. arc separated by a 
gns-tight partition, and if tho gas is not a 
saturated vapour, .tho pump will diminish tho 
pressure In tho L.P.V. and increase it HI tho 
H.P.V. ; it will act at tho same time as a 
compressor and as nn evaouator. In practice 
one of tho two vessels is almost always main- 
tained at atmospheric pressure, and variations 
of pressure in tins other vessel alono arc im- 
portant, If this condition is fulfilled, a com- 
proBsor may lie defined as R ])ump of which 
tho L.P.V." is at atmosphorio pressure, an 
ovacuator as one of which the H.P.V. is at 
atmospheric pressure. 

Tho L.P.V. ami H.P.V. arc aclclom com- 
pletely separated, oxcopt in laboratory evacu- 
ates ; there is a continual stream o gas 
from ono to the other. If tho energy re- 
quired to produce this stream ia comparable 
with tho wholo work done on tho gas, ^tho 
pump may be termed a " blower," or, if it is 
of one constructional typo, n, " fan." The 
distinction between pumps and blowers, 
though formally indefinite, is perfectly clear 
in practice. Blowers are usually, but not 
always, compressors, producing pressures 
fciwtor than atmospheric. In blowers there 
can be no single and definite p n or p r ,, capable 
of general scientific definition ; but there ia 
usually some pair of places along tho stream 
of gas passing through tho blower at which 
it is obviously convenient to measure pu and 
p L . These places may bo regarded for our 
purpose ns constituting the fl.P.V. and L.P.V. 
(2) NOTATION. Suffixes L and II denote 
quantities retort-ing to tho L.P.V. or H.P.V. 
Many of tho formulae given will still ho true 
if tlics suffixes L and H are interchanged j this 
foaburo is indicated by writing before them 
{" L or H "). " 

P, yt, j)n =prossuro, 

= initial pressure (tho same for 

L.P.V. and H.P.V.). 
2'j,, j)n = final preasiu-es. 



T n TT. Tn = absolute temperature of atmo- 

sphoro, UP.V. aiid'H.P.V. 
m = mass of gas. 
IP velocity. 
S volumetric speed. 
W = work. 
to power. 
p~ density. 
ij = viscosity, 
e = friction cooflieiont. 
15 = 'JSmecii. = moohaiiical ofTiciomsy 
E,, (ll = volumetric oflicionoy. 



n=atmosphoric pressure. 

P= vapour pressure. 
V Tl( Vn = volumes of L.P.V. and H.P.V. 
iii,> MH= maximum and minimum volumes 
of " cylindor." 



(3) WOHKINCl 

may be distinguished either according to then- 
working characteristics or according to tho 
principleo on which tho action depends. Of 
tho working characteristics tho following aro 
tho most important of thoso applicable tu 
pumps ol all types : 

Range of Pressure. ft any pump bo worked 
continuously between closed vessels, there will 
ultimately Lo established in them constant 
pressures, p n , pi?. By tho range of pressure 
is meant either (a) tho ratio j>ii /V, ()l ' ( 6 ) tll(1 
difference jj,,' - V- (<0 generally tho nioro 
important quantity and will hero ho termed 
the " range," denoted by K i for it oftou 
approximately independent of tho absolute 
values pn, P*>- But it is never completely 
independent; for all pumps havo a minimum 
fcolow which they will not reduce pr. what- 
ever is the value, above this limit, of ?>, 
and all havo a maximum pa, though it 
may bo determined only by mechanical 
strength. 

Tho range of a pump of any given typo 
may be increased by working two or mwv 
similar pumps in series to form a " compomtci 
pump, the L.P.V. of one being tho II.I'.V. ol 
tho next. In all important eases, tho iunin 
of tho composite pump is approximately or 
exactly tho product of tho ranges of tho 
components. But a composite pump can 
also ho built up of components of difforont 
types ; no general statement can ho miulo 
about tho relation between tho range <vf 
such a composite pump and thoso of its com- 
pononts. 

(4) SPEED OF PUMPING. Tho snood is 
the rate at which gas is transferred from 
tho L.P.V. to tho H.P.V, The amount uF 
gas is usually estimated by its volume at blio 
pressure of tho L.P.V.,- whether the pump IH 
a compressor or an evacuator. Tho H|i<n"l 
so estimated is called tho " volnmotrii 
speed," S, and is expressed in volumo \it 
unit time. 

Measurements of S aro usually 
observations of tho change of p\ t \ 
pressor or of ps, in an ovacualor, tl. 
or L.P.V, being completely closci; 
during tho measurement is email I 



AIR-PUMPS 



3 



with p or pi,, tho gas may bo regarded as 
perfect, Consequently for nn ovaouotor 



In a compressor, pi, is constant and equal to 
II. Therefore 

s= . . . . w 

In blowers tho volume involved in S is 

usually estimated at p K . It ia conveniently 
mensural by some typo of flow-motor placed 
in tho outlet or itdet pipe. If tho pressure 
at fcho point whore the meter is placed differs 
considerably from Pa. a corroetiou must ho 
applied to tho readings of tho motor. 

S is usually a function of pu and pi 
aa well as of the nature of tho pump ; hut 
there arc important exceptions. Tho range 
K or tho maximum difference of pressure 

00 



(3) .applied to an evaouator ov compressor 
becomes 

(LorH) W^^Vn-^ - (' 



If II - 



smilll > ( 5 ) 



(LorH) 






that s=o. , ,. . , 

g (5) THE KFFroiENOY. Several kinds ot 
efficiencies MO recognised as applicable) to 
pumps ami blowers ; of the tho mechanical 
pmmcnoy, or tho ratio of tho useful work 
ilono to the total work expended, ia alone 
applicable to all types, Botii terms of the 
ratio need further definition to rid them of 
ambiguity. Tho work expended ia usually 
taken to mean either () tho work expended 
on tho gas in (jiving to it energy, com- 
pressivo, kinetic, or thermal, or (6) tho worlc 
supplied to tho mechanism of which the 
nump consists, including that lost in fruition 
of wlid or liquid parts. Tito olhoionoy 
reckoned with (a) to oflen termed tho 
" gas " efficiency ; that reckoned with (b) 
the " ovor-all " efficiency. 

In pumps, where the L.P.V. and Il.P.V. s 
are separate, the useful work is always taken 
to be that required to transfer tho gas that 
IIRH actually passed from tho former to tlio 
latter. This work will be least if the trans- 
ference is effected rovermbly ; if tho L.P.V. 
and H.P.V. are at the sumo temperature, tlio 
revorstblo transference must he isothermal, 
and any change of temperature during the 
process involves tho expenditure of more 
work. If the transference is rovcrsihlo and 
isothermal, tho work required to transfer a 
mass of gas between tho atmosphere at con- 
stant pressure II and a closed vessel, the 
pressure in which ia changed by tho transference 
from H to p t , is given by 



whero V = fij) is t" isothermal wharnotorlBtio 
of the mn'sa of tho gas occupying the elmcd 
vessel at tho pressure p,. If tlio giw IB perfect, 



If pjl ia small, as in a high ovacnaUir, it- 
becomes ,_, 

In aomo text-books, tho work dono by tlio 
atmosphere is left out of account; the term 
in II is omitted from (3), and tho second and 
third terms in tho bracket from (B). J*ul 
since work is always dono by o.- on the atmo- 
sphere in compressing or evacuating, the 
efficiencies reckoned without those terms would 
Boom to have no practical significance. 

In Unworn tlio useful effect is usually 
estimated by tho volume of gas produced _at 
a eivon pressure. The work required to force 
a mass o( Rtw from the atmosphere into a 
vessel in which, tlio pressure IK mmntfimed 
constant and ei|ual to p n 0>y iiwrPHBinf^ fchfl 
volumo of tho vessel as the gas enters) w Riven. 

y _.,- /m 

where V is the volume of tho pas at pressure 
MI,. Consequently, if" 8 is the volnmolno 
aiiced, and w the work dono per second, 

a^n-lLJS. . . (0) 

Tlio stream of gas issuing from a blower 
possesses kinetic energy. It tho worlc ex- 
pended in giving to it this cncirgy >" *<> ' 
included as useful work, there numb ho added 
within tlio braokot in (0) tho term p v = W> 
It is often impossible practically to convert 
this klnotto energy into energy of any ot>or 
form without stopping tho flow which m the 
main purpose of tho blowor j accordingly t!io 
total efficiently, as it In called, reckoned from 
tho relation , , 

ia often miHleadmg. Hnt it may ho nntod 
that ideally it in always possibl.! to reriuco 
p , to Koro without ehanp;inp; S, anil thus to 
"'convert velocity into prt'HSiirn " ; !<' 
the orose section of tho Btream is mtwlo 
infinitely largo, an infinitely smnll v will give 
n finite S, 

In addition to tho mechanical cJliciomiy, 
them ia recognised for many pumps a quantity 
known as the volumetric offlutonoy. Hut wnco 
this quantity cannot be defined ((onorally lor 
all types of puni]i, it will ho discumird in 
oonneotion with thoso to whioli it - 1 '"" 



AIR-PUMPS 



(II). Tho remaining working i;luim<itemtics 
ooiniiiiMi to all pumps aro Iowa ciipahle of preeiao 
nuMSHrtmiont j but they nm mnw the less 
important. They includo simplicity and tson- 
voiuonec!, lii'Ht coat and cost of maintenance, 
adaptation to availo-Wo sources of power, and 
NO on. WhoH sovoivtl types of ]HJJii{) an jir- 
ini!tihlo, it ia usually those chmuo tomtits 
mthor tliau uny measurable) efliiupnoy which 
tlotormmo tho elioico. They will bo noticed 
in <j(i(irifl(!ti(Jii with [KH'tioiiliir tyjjejj. 

(V) .l.'inNcii'Li'is OF AOT.ION. .I'Viv tho 
t'lotiuled consideration of tho various types of 
pump, it in KIOTO uonvcnicrUj to adopt a 
olfiHsifumtion fjasfid upon tho principles under- 
lying tlio notion, Hero pumps fall into thi'co 
great 



A. Aerostatic. 

B. Aerodynamic. 

0. Molecular or Hi&h-v;umum, 

In mi ei/fl(i'fi pump this transforeniio of 
gust is o (Touted l>y forties that arc at any instant 
in aliii-itml or/ nil iljri urn. Kt>!' uny }w'tieu]ar 
pump bins raiif-o of pressure ia independent of 
thn n|i(!dd i> working witliin wide limits ; tlio 
)niiiip nan Iio worked infinitely slowly without 
IONS < ?'ftny or of oiTioionny, (This atdtomenfc 
ia not Htriclly triio wlion tho viscosity of n 
hdivitiafcing liriuid its used to Becnrc gas- 
fuiuh pumps am dynamic, lint not 
In ;tll {micticjil oxftinplcs filto 
statical (orces aro those duo to comjirftssion, 
lint thoso duo to ohangn of tornporafcuro might 
wiH!iMvaI)ly h used. 

.lu cut ae.fO(ltjRttmie- piutiji tlio forces <m tho 
(,'iw aw iVyimmiuii), and vary witli tlio motion 
u tho purU of tho pump; they coaso whon 
tho apnfttl nf working heciomcs itiliiiitoly sinaH, 
HCI tliat tlio range and sjrertrl (F tlio pump 
vanish Loyotlior. Those dynamical forces 
from tho inortiti or visooaity of the 



but will ho conveniently noticed briefly at tho 
end of this article. 

A. AllKOSTATff! l.'HML'fi 

(8) HANOI-: AND (-jr-KHi). Tho working part 
is always a vosstit (U) of variable volume, u, 
Ui.s 

(!) (miH!tecI to tho L.P.V, when it 
volumes 19 a maximum i, ; 

(2) distsonncoted from tlio L.I'.V. and the 

volume decreased to tho minimum ui\ ; 

(3) connected to the H.J'.V. ; 

(<i) diBComiocted from tho H.l'.V, and tho 
voluino increased to.[ |P 

This ideal oyclo is never attained in praetieo 
but forms tlio basis of any calculations. 
Kvon if tho ideal eyob were attainod, tho 
general formulae giving tho K*]lioti botiwooii 
pu, pi> fla after a number of cycles n would 
ho nxtremoly complicated. -lint if it is as- 
sumed that the (fiis is perfect, and that tho 
transfereniici in isothermal, tlio relation liotwwm 
(?}([) and (^n)f the. vivluea of pn after 
tho >ith and {-H-i-])th cycles, ia 

(L<irH) (./(,,^^^1^-Xul^iIli. (1) 
Mi''' "n 

In a compressor or evacuator wo havo from 
(10) 

fi"n1 r 

' i ' w "> -fK 



'('(IP (Itstinclion IwUvooii fclio two classes 
unn bo oxiH'OSHod liws furiiiftlly, hut noiJiftpH 
inoro oltinvly, hy Haying that in thn first oluaa, 
bub not in tlio Ncuond, liho acition la " jmnitivo " 
in tho ong.incoi'iiiK HIUIKH ; <ir that, wliilo it in 
impossible to blow fcliroiigh a pump of ilio 
firat class, it in possible to blow through <mo 
of the sooond. 

In hotU thoBO tifasaos tiio forces aro umih RH 
nra asawiatol ivitli a oontiiniious modiiiiH. 
In tho HuMl class tins notion is duo to " forcca " 
ajiproeiixblo on tho motconldi 1 but not on tho 
innltu 1 scute. Tho clasH would properly bo 
termed " mdositlfir" but sinco that town 
has hcori ttjiproprmtod to a jinrtioutar member 
of it, tho 1m soioiUifio expression " high- 
vasunm " pum])3 will ho used, 

In ntWition t thcso tlirco classes of pump, 
aro some methods of ovivmiation which 
ly satisfy tlio doflnilion of pumping, 



(11) IH trim wliatovor tho ratio of n to tho 
Vs ; if it is small and if N, tlio niiiufior of 
Rydi'.s [U' unit of time, in )/ujo, (11) 



(12) 

Proiw (12) mid (1) wo obtain for Uio volumotrio 
spend of an ovaouator 



and for thnli of a 



Tlio lutigo of presstii'o is given Ity iS 0. 
Consoqiiontly 

(LorU) *?*~l\ . . (IB, 

The mngo, measured by the ratio of tlm 
preshnvcH, i independent of tho initial preHHiiro 
ami of Clio volumes of the L..P.V. and II.C.V. 

TJiflso relations become voiy nimpln ivlioti 
HII, tho voluino of tho " dead spaco," in wint. 
Then (ll)-(l'l) Iwoomo" 

vl- = 1 + rt (eoinprossor), . (1/1) 
11 Vii 



AIR-PUMPS 



? 'f' 
11 



' 



(17) 



H Nit (l (compressor), . . (IS) 
V r , 



(evacuator). 



(10) 



Thus the volumetric speed of such a pump 
woidd bo independent f tho pressure against 
which it worked ; its ningo would be infinite. 
(()) VOLUMKTUIO EWJOIUNOY. In no 
actual pump ta tho ideal cycle performed : 
the yield is always less than that given by 
(lO)-'(H), and it fortiori less than that given 
by (l")'(l") tm k'io assumption of no (load 
space. The deficiency is due to incomplete 
" connection " and " disconnection " of the 
L.P.V. and H.P.V. with U and with each 
other, i.e. to leakage and to a failure to 
establish pressure equilibrium. 

Tho comparison of an actual witli an ideal 
pump is made in terms of tho " volumetric 
efficiency" (K v ,,,.), wliioh may bo roughly 
defined 'as the ratio of the number of cycles 
in which an ideal pump would produce a 
given efl'ect to the number of cycles in which 
tho actual pump produces the same effect. 
Tho ideal pump ia assumed to have the same 
"i. (<!.;/, cylinder volume) as tho actual pump ; 
it is 'also usually assumed to have no dead 
space ]T . This last assumption is not 
necessary, for tho often t of tho dead space can 
be readily calculated if the pump is otherwise 
ideal ; but in the pumps for which the 
conception of volumetric efficiency is most 
important, KH is always made as small as 
possible, and its magnitude is important in 
judging the excellence of tho design. 

The " efl'ect " by which H vill . is estimated 
must bo defined. It is usually either (I) the 
attainment of a given j>ij\l or p a {n, or (2) 
the transference of a given quantity of gas 
with a llxed j>i, r pn. In either case, J3 vl ,i. 
is a function of ?i|, or pn, and the value of this 
pressure must he staled. l''or a given pi, or 

(])'und"ror(2). 

If (1) in adopted, and if n is the number ot 
cycles in whioli the actual pump establishes the 
assigned pnjtt or j^/ll, then from (1(1) and (17) 

. - (20) 



. (21) 



. 

If (2) is adopted, and if N is the number 
of cycles per unit time required for a given 
volumetric speed H, wo have from (18) m (10) 



(evacuate). . (28) 



IE the H.P.V. or .LP.V. is not at atmospheric 
temperature, (20)-(23) must be corrected by 
tho substitution of Vji/T H , V],/T(., KL/TO for 
Vn, Vr,, ?(r : . 

(10) OTHER CIIAUAOTKKISTIOS. The ad- 
vantage which aei'ostatic pumps possess over 
other types lies in the great range which can 
bo obtained with them. They are, therefore, 
well suited for the production of very high 
or very low pressures in a single operation ; 
but extreme pressures can be obtained with 
other types combined into composite pumps. 
They are in general less well suited for tho 
transference of largo volumes of gas under 
moderate differences of pressure, although 
sonic types (Ac, d) are used for this purpose. 

Their disadvantage is that they cannot ex- 
haust vapours satisfactorily, especially when 
designed for a large range, for the vapours 
condense in U when its volume is reduced 
and do not pass readily into the H.P.V. ; 
when tho volume is increased again, they 
evaporate once more, return to tho L.P.V., 
and keep p tt permanently at or above the 
vapour pressure of the substance. Permanent 
gas mixed with tho vapour is removed very 
slmvly after its partial pressure in the L.P.V. 
has fallen to that of the vapour. 

The various typos of aerostatic pump are 
distinguished by the construction of U and 
tho means adopted for connecting and dis- 
connecting it with the L.P.V. and H.P.V. 
The following sub-classes include conveniently 
all tho important typos : 

Aa. Solid Piston Pumps. 
Aft. Liquid Piston Pumps. 
Ac. Moxiblo Container Pumps. 
Ad. Rotary Aerostatic Pumps. 

A. Solid Piston Pumps 
(11) Tim VON GUKBIOKE PUMP. This is 
the oldest typo of gas-pump, and its invention 
is generally attributed to Otto von Guericko 
(1072); it was probably developed from the 
similar water-pump. It has still a wider 
sphere of use than any other type, being used 
for tho attainment of pressures from 1000 
atmos. to 10- a mni., and for volumetric 
speeds from many cubic feet to a few cubic 
millimetres per minute. It is equally familiar 
in heavy engineering, in delicate laboratory 
work, and, as tho tyro pump, in everyday 
life. Broadly, the advantages of tho type 
are a great range of pressure and great 
mechanical strength j the disadvantages, cum- 
Immsness and mechanical inefficiency. It is 
unrivalled for high-pressure compressors, and 
for small portable laboratory ovaeuators j for 
ail other purposes it can be replaced by 
other types. However, it is still widely used 
oven for blowers, the purpose for which its 
disadvantages as compared with other types 



G 



AIR-PUMPS 



arc most innrliocl. Its survival is probably 
due partly to its long history and l:o its re- 
Homblftnco to the reciprocating steam -engine, 
ut which tho constructional problems have 
been studied so completely. 

Tho principle of the pump is familiar to nil. 
The vessel U is a cylinder in which moves a. 
piston. Connection is made to the L.P.V. and 
II.P.V. either (a) through ports in the cylinder 
wall opened and covered by the piston, or (6) 
through valves moved "positively" by the 
piston or tlio mechanism that uetnatcs it, 
or (c) through valves opened and closed by 
tho oxeeas gas pressure, (c) in tho oldest 
arrangement and Hie simplest to construct, 
hut it represents it dopiu'tiire from tho ideal 
cycle and necessarily reduces tho range below 
the ratio u^n ; for the connection between 
TJ and tho L.P.V. or II.P.V. ceases before the 
pressures have become equal. It is still 
standard piwM.icoinliigh-prossuroeomprc; 

in ovacuators for moderate vacuii (ft) IB often 
used ; in those intended for tho lowest possible 
' pressures, ono at least of tho valves must be of 
typo (ft), 

(12). Throo kinds of piston pump may 
he' considered rather more fully. The Aif/A- 
pressure cowpre-isor, shown diagram miitieally 
in Fig. I, is nlways composite. It would not 
be impossible to' obtain a range of pressure 




of 200 and a final pressure of 200 atmos. by 
a simple pump, hut there are several reasons 
why tho multi-stage puni]) is preferable, 
Thus, it is possible to cool the gus between 
the stages by the " Intel-coolers " 0. Jiy 
spacing tho cranks evenly round the crank- 
abaft n, more oven torque anil a balanced 
motion ean bo obtained, Tho construction of 
eiioh pump can ho adapted to tho pressures 
between which it has to work ; the thickness 
of tho metal can bo increased, as shown in 
tho figure, as tho pressure increases j special 
piston packings and forced lubrication can 
bo used in tho H.P. cylinders. Some makers 
prefer water to oil as ft lubricant nt high 
pressures, and at the highest pressures the 
substitution seems necessary because oil would 
burn explosively. 

Tho volumetric efficiency of such a punir 
should be wit less thmi 80 per eont ; the gat 
efficiency also about SO per cent ; and tho 
ovor-all' efficiency about GO 'per cent. Tho 



vork done on tho gns may bo measured, for 
iho determination of the gay efficiency, by 
ndicator diagrams taken from the cylinders. 
These oflidciicies arc determined largely by 
the completeness of the cooling, which is ono 
if the most' important features of these 
jumps ; they are also determined by leakage 
ind by throttling at the valves. 

(l';j). _-/<'/(/. 2 shows a largo-scale two-stago 
ovaonator, such as is used for the condensers 




of steam-engines and for working pnonmatio 
tubes. Tho slide-valves are similar to those 
of a Bteam-engino, but to secure smooth, 
working connection is made between tho 
L.P.V. and tho II.P.V. when the piston is in 
tho extreme position. Tho pistons are con- 
nected in tandem. If tlio pump ! to ho 
worked by a reciprocating sl:oain.ougino it 
would be possible to use the same pmlon- 
rod fop the driving piston, und thus to avoid 
rotary motions and bearings and to reduce 
moving parts to a minimum ; but this arrange- 
ment ia seldom adopted; pump and motor 
are usually separate. 

Tho volumetric offioionoy should bo about 
8fi per cent when ^, = 20 cm. of luorcury or 
moro; about 80 per cent at j)i-===r> em. j for 
lower values of p,., 'ICi. will fall rapidly, 
and ?)], will not be less than 1 om. Tho 
over-all efiioiimcy should be ixot loss than fit) 
per cent at tho higher pressures. 

(Ij.j.jf.'iV/. II shows part of a laboratory 
cvnc.unlor in Very general use. Tho pump is 
composite with two stages ; tho high-pri'Hmiro 
member presents no special features and in 
not shown ; it is connected to It. In tho 
low-prossure member shown, tho piston is 
covered with oil which is ejected at tho end 
of tlio stroke through tho valve V, carrying 
the aii- with it. At tho sanio time the eraitk 
J, worked by tho piston guide 1C, forces oil 
into tho space by means of tho oil-pump H { 
from tho oil flows on to tho top of tho piston 
as it descends. It is claimed that tlio pump 
will attain 10' mm., it tho gas and oil are 
free from vapour. A drying tube with .P B 6 
is necessary in the connection L to the L.P.V., 
and another, which can bo filled with ()a(.!t a( 
is desirable in the outlet of tho H.P. cylinder 
to keep tho oil dry. The pump la very 



ATR-PUMPS 



efficient find convenient clown to 
of ()!)! mm., but to obtain the highest vauua 
of which tlio pump is capable needs groat 
care in its treatment. 

A piston ])ump for extremely low profistu rns 
]ias alHo been developed by Gaedo 1 (1) i i" 
principle it (loos not differ greatly from tlmt 




1'KI. 3. 

shown. In order to free tho oil from water, 
and thus to dispense witli a drying agent, 
tin) oil in forced through a special woven 
material which effects a Hepuration of tho 
two liquids. Gaedc chums thai his jminp 
without, luiy drying agent will attain a pressure 
of 1C" 6 mm. 

Aft. Liquid Pinion Pumps 

(15) ToiutinKLT.i'H l?iJMi'{2),(3).It is im- 
possible to make a perfect fit or a gas-tight 
joint botwocn solid bodies movable relatively 
to each other ; and therefore all truly solid 
piston pumps have some leakage and Homo 
dead space. Leakage can bo wholly prevented 
and dead apace very nearly abolished by using 
a liquid in plauo of a solid for tho moving 
portion of the vessel U. The ratio (p|[ n /J>r,) 
ean bo increased by the substitution, and 
higher vacua (or higher compressions though 
this result is not so important practically) 
obtained in a single operation. In fact a 
liquid is actually used in this manner in 
pumps which are usually regarded as of the 
Holid piston type. Tn tho pump described 
last, the oil "covering tho " piston " _ and 
passing through the valves is really tho piston, 
and the mine purpose is served, in part at 
leant, by tho lubricating liquid of othei 
pumps oE section A. However, the typioa 
iic|iiid piston pnmjis wore developed historie- 
ally from Torriedli's, and not Oiierioko's 
method of evacuation ; and the dislinetior 

1 FlKiires In lirnoliotH refer l rpfercniifiH at llio OIK 
oE lliu urtk'le. 



letween solid and liquid pistons, thoiigb 
Hglit from tins Htand point of seicntifif! 
iipld, is ]ierfti(;tly ehai 1 in Jill practical 




In the Torricellian pump the vessel to bo 
ivammlod is completely Tilled' with a liquid 
if density />; tlio open end in placed beuoath 
iho free surfaces of a liquid, which in usually 
;lie same as that filling tho vessel. If, in 

his position, nuy part >f 
,ho vessel is at a height 
tbovo the free liquid mir- 
'aco greater than Ii , where 
i pf/ (11- T), the surface 
if 'the liquid will shik to 
tho height A a , and tho 
ipper part of tho vesaol 
vill contain only tho vapour 
of the liquid at tho pressure 
. corresponding to tho pre- 
vailing temperature. As a 
iquid for such a pump, j-,.^ 4 _ 

norciiry is especially suit- 
able, both on account of its high density 
and small "barometric height," fi , and on 
iceount, of its low vapour pressure. 
This method of evacuation has tho obvious 

lisitdvantage that the wliolo L.P.V. lias to 

ie filled with liquid and inverted. A very 

ibvioim imidilieatio!) of 1C was described in 
lirineiple by flwedonborg (1722) and put into 

i practical form by downier (18SI>). The action 
is clear from ./''iff. * ; tho 
moreury, is alternately raided 
and lowered and the two- 
way cock alternately con- 
nected to the- air nncl lo 

tho vessel to lie evacuated. 

Tho pump is a true liquid 

piston pump, differing from 

Cliioricko's pump only in 

this nature of tho piston 

and tho valves. 
(10)TirTPT.miPwMr. 

A greatly improved form 

of tho pump originally duo 

to Toplor (4), but realised 

pmetieully by Hagen anil 

Necson (5), in shown in 

./''iff. fi ; no stop-cooks are 

required. It was iitnid in 

many classical rcHom'ohca 

on low vaisiift at tho end 

of tho nmotocmlh eentury, 

being at that time rivalled only by 

Sprenp;el pump (see below) afl a means of 

attaining low pressures. 
]}y raising tho reservoir A, mercury is 

driven up into tho cylinder B, thereby dvivinp 

out the gas from the cylinder through the 

capillary tuho (', from which it may ho 

colleiibii'd in tlio mercury trough. Moreury is 
prevented from llowiny; over into tho 




AIR-PUMPS 



to bo exhausted (V) by the snio.ll glass 
valvo 1). 

On lowering tho reservoir, Uio mercury 
flows hack from tho cylimlcr, and when tho 
mercury reaches tho lower purl of tho cylinder 
gas will cuter 'from tho vessel V througli the 
side-tuba E, ready for expulsion at tho next 
stroke, 

Tho lower! tiff of tho reservoir muat lie done 
very slowly so long ns tho pressure in V is 
more tlmn 2-3 mm., otherwise air entering 
tho cylinder through the sido-tubo E will 
carry mercury violently up tho tube I* 1 , and 
this may easily shatter tho glass-work of tho 
cylinder. 

When tho vacuum becomes liigli, tho 
raising of tlio reservoir must be done very 
slowly, otherwise the " luiniinor " of tho 
mercury at tlio lop of its travel in the cylinder 
will break the cylinder head. 

Tho reservoir A should have about twice 
the capacity of B. Tlio volume of tho cylinder 
B is fixed by the work required from tho pump, 
but in ordinary laboratory models is from fiOO 
to COO c.c, Tho capillary tubu is about 
800 mm. long and 1 ram. boro. Tho tube I? 
should have a boro 12 nun., and fcho lube E 
about 4 mm. This ensures that gas entering 
from E to I? will tend to travel in bubbles 
upward through tho mercury in P, instead of 
carrying the mercury solidly up with it. 

The P a O B tuba is, of course, inserted to 
absorb water - vapour, which presents tlio 
same obstacle to this as to all aerostatic 
pumps. 

Tho lowest pressure which it is possible 
to obtain with this pump is determined as in 
(IB), by the ratio u\,ju\\. u\, is tho volume of 
B, while u\i is tlio volume of tho smallest 
bubble which the mercury will carry down the 
capillary C'. This volume is approximately 
that ' enclosed bntwnon tlio convex surfaces 
of two moron ry jrinniseiispH which just touch ; 
it decreases with the bore of tlio capillary. 
But there is some gas adhering to the glass 
in addition to actual bubbles left behind by 
tlio morcnry, which makes it useless to decrease 
tlmt bore beyond a certain limit. Tho lowest 
pressure recorded as nltalnod by a To'pler 
pump is 0'00002B mm, in addition, of course, 
to the vapour pressure of the mercury. 

Tho working of a Toplor by hand is extremely 
tedious, for several houra may ho required to 
reach tho limit of pressure. Numberless de- 
vices for rendering its action automatic have 
been proposed ; electrical contacts worked 
by the mercury, or else tho weight of tho 
mercury, are used to- control tho operation. 
But no description of thorn is necessary 
to-day, for tho problem of the automatic 
Toplor seems to have been solved fhmlly by 
(facile fG), who proposed to move tho solid 
vessel mthoi 1 tlmn tho liquid piston. 



(17) GAEDIJ ROTARY MKIICUKY 1'irnii 1 . 
The general action of the pump can bn Keen 
from .Fiys. 0, 7, which ai-o vertical sections 
parallel and at right angles to thi! front of the 
pumps. The outer casing A contains mercury 
to about two-thirds of its height, ami i.s 
connected through the pipe B with a rough 
vaninim pump (e.g. an ordinary piston pump) 
capable of nmmtaining a pressure of about 

fl! 




10 mm. An ingenious device shown in ffiff. 8 
is used for cutting off the rough pump after 
the preliminary exhaustion. Inside this casing 
rotates a drum .B, made of porcelain, to tho 
side of which is attached a smaller porcelain 
drum C. Tho two drums communicate 
through tho port D. 

It will bo soon from this diagram, that if B 
is rotated in tho direction of the arrow, the 
portion of B above the mercury will com- 
municate with tbo pipe V, connected to the 
vessel to bo exhausted, so long as tho purl .1) 
is not immersed. As soon as .1) is immoi'Hcd, 
tho communication with V is closed, and when 
tho tail end 13 of tho drum rises above 
the mercury, tho 
gas will bo passed 
on to tho rough 
vacuum. 

In the pump 
as actually mami- 
faetiirod two or 
three drums arc 
spaced symmetric- 
ally on the same 
axle ; a second 
drum is indicated 
by tho dotted lino 
in Ififj. 0. Tho speed of tho pump is thereby 
increased, but the construction made much 
more complicated. 

Tho range of tho Oaodo pump is probably 
somewhat loss than that of tho Toplor, for tho 
conditions for the expulsion of small bubbles 
from U are loss favourable. But since p n n 
is loss, owing to tho use- of tho auxiliary pump 
and since its speed is much greater, the least 
pressure practically attainable in at leant as 
low; a pressure of 0-00005 mm. is well within 
its power. The volumetric speed is not con- 
stant, as it would bo according to (10) ; it 
is about 110 om, 8 /sco. at 0>01 mm., and falls 
of? continuously at tho lowest pressures. 

_ (18) TUB SPHENOID PUMP. A liquid 
piston pump, using mercury but working on 




AIR-PUMPS 







a somewhat different principle from those 
just described, was invented by Sproiigel in 
ISfifi (7). It lias over the (.ieisslor (and Inter 
Toplor) pump the greater advantage that its 
notion is more nearly continuous and auto- 
matic, Tlio gas is carried out of tlio L.P.V, 
by tlio fall of mercury down a capillary tube, 
as in tho Toplor pump ; but it is not forced 
into that tube ; it enters tho tube under the 
pressure in tho L.P. V. and is there trapped 
between successive drops of mercury falling 
into tho top of tho tube from a reservoir. In 
another and more convenient arrangement (J^V/. 
9) tho drops arc formed in the capillary by 
tho entrance of gas from tho L.P.V, through a 
side tube. But tho principle is the same ; 
the liquid column in the capillary will break 
up into drops, trapping the gas between thorn, 
if tho gain in surface tension energy duo to 
tho formation of a liquid-gas surface is greater 
than the loss in hydrostatic energy duo to 
the accompanying displacement of tho liquid. 
Tho precise calculation of the conditions for 
drop formation is complicated ; lint ifc is 
clear that the bore of the capillary must 
bo below . tho limit at which drops could 
lio formed in tho tube without completely 
occupying its cross-section. 

Tho volumetric speed of a " single-fall " 
Rprongol is oxtromoly small, not moro than a 
,._.._., few cubic millimetres por second. 
It can be increased by connecting 
in parallel several capillary tubes 
all foil from tho samo reservoir, and 
thus making a " multiple -full " 
pump. The lowest pressure attain- 
able is lixed by tho samo considera- 
tions as in tho Toplor pump, but 
it may bo increased by small 
quantities of air carried into tlio 
vacuum by tho stream o mercury 
from the reservoir exposed to tho 
atmosphere. Many devices liavo 
been suggested for avoiding this 
defect. (See (,')).) 

Tlio Rprongol pump ean be made 
completely automatic, if it ia 
arranged that tho mercury which 
has fallen down tho capillary IB 
restored periodically to tho reser- 
voir. Such an automatic form was at one 
time in universal use for tho exhaustion of 
electric lamps (8). It is shown in Fig. 10, 
and the method of operation is obvious from 
that figure. 

Tho outlet is connected to an auxiliary 
pump maintaining a pressure of n. few cm. 
Tho capillary fall tubes A, into which mercury 
flows from 1) through the jets 0, aro therefore 
relatively short (about 20 cm.). Tho bent 
tube '\\ enables the end of tho exhaustion 
to be seen by tho disappearance of gnu-bubbles 
from tho meroury. 




I'm. JO. 



The reservoir E ia normally connected to 
IT ; an occasional admission of air, in in-dor to 
rcatoro tho mcreury to ."!>, is controlled by a 
dimple timing device set once and for 'all. 
It can also ho controlled by the weight of the 
mercury in tho reservoir. 

The common laboratory mercury still is in 
effect a Sprongel pump whereby gases intro- 
duced by the mercury are removed. 

For high-vacuum work, mercury pumps of 
these types, with tho possible exception of tho 
Gaedo puni]), are 

obsolete, and re- |[ H 

placed by those nf 
Class 0. They 
may, howover, bo 
used as auxiliary 
pumps in series 
with those of that 
class when it is 
desired to collect 
gases pumped out 
from a vessel. For 
this purpose 
tho Toplor Jj=_ 
pump ia most 
suitable. 

(19) OHHHIOAL 

AND OTHEIl PUMPS, 

The foregoing 

pumps aro designed to attain low pressurm 
But liquid piston pumps aro alno o sorvico 
for pumping chemically active gases, which 
would attack any of tlio metals or other 
materials suitable for the construction of 
solid piston pumps. Thus for the compres- 
sion of chlorine, pumps uro used of which the 
cylinder and valves are made of load-covered 
stool, whilo the piston consists of oil or sul- 
phuric acid. Tho liquid piston is Hot in 
motion either by compressed air or by a solid 
piston working in one limb of n IJ-tilbe, tho 
other limb of which is tho chlorine pump. 

Laboratory pumps essentially similar In tlus 
Toplor, but using oil or glycerine or sulpburii! 
acid in place of moroury, have also boon used 
for some purposes. The lower densities of 
theso liquids enable tho pumps ti> be umdo n( 
glaast with a volume much greater than that 
sot by tho moolmnical strength of tlio glass if 
mercury were used ; or bho gun to be pumped 
may bo ono which attaolm mercury. 

Again, air compressors for high prefmuroH 
have been constructed in which water is used 
as tho piston in order that the cooling of tlio 
gas may be more efficient. I" some of tht'so 
mctal chains hanging into tlio water from the* 
top of tlio piston have l>eon used to faoilitato 
tht! transfoTonaa nf boat between tlio gas and tho 
liquid. 

Ac.. Flexible dan lantern 

(20) BELLOWS. In theso pumps tho vessel 
U has flexible walls and Ha volume ia varied by 



10 



AIR-PUMPS 




Fiu. 11. 



changing its shape, Tho advantages of the 
typo arc high mechanical efficiency due to 
tho ftlHonco of friction, simplicity of construe- 
tion, and consequent cheapness and reliability. 
On the other hand, they have a small range 
of prcasure, partly because tho ratio MH/MC, 
is comparatively groat, partly because tho 
flexibility of iho walls makes it impossible to 
nan them at pressures differing greatly from 
atmospheric. They arc usually made for hand- 
working or very lew power mechanical drives. 
Tlio earliest 'examples of tho type are tho 
lunga of air - breathing animals ; tho later 
improvements of tho 
original model for this 
pui'poao arc insignificant. 
The type is almost 
equally familiar in bel- 
lows of all lands, for 
blowing up a lire, for 
vacuum cleaning, for 
piano -players and squeak- 
ing toys ; in the fountain- 
pen filler, now partially 
replaced by a piston 
pump ; in the bulb for 
scent and other sprays. 
But it is also used for less commonplace 
purposes. 

The action of Iho blacksmith's bellow^ is 
shown diagram matically in Fig. U. The 
end plates A and C arc fixed, while B is given 
EL reciprocating motion. Some bellows of tins 
kind for smiths' hearths are several feet in 
diameter, with the flexible sides of leather. 
The air is usually pumped into a reservoir 
bellows in which a pressure of about in. of 
water ia maintained by a weight. 

Fig. 11 also represents, on a different scale, 
a useful laboratory imnip. Tlio bellows arc 
hero made front tho inner tube of a motor tyro, 
tho corrugations being obtained by largo metal 
rings inside the tubo and small rings outside 
placed alternately. Tho cylindrical discs A, IS, 
C are of aluminium, and U is driven by a crank 
Irom a small motor, 

(21). The most elaborate pump of this 
nlaaa is the organ bellows, shown on Fig. 12 ; 
the bellows com- 
pressor, called 
tho " feeder " 
hollows, ia at 
F. The upper 
board A of the 
feeder is fixed 
and the lower 
board Bislnngcd 
to A by n. leather 
joint. Tho 
wedge-shaped 
volume between A and 11 ia enclosed by the 
wooclou ribs R ; tho riba are hinged to each 
other and to A and H with leather and cloth 




Tho board B fulls by its own weight and_ the 
air outers through the fiat valve V,. Air is 
compressed in the feeder by a hand lover, 
and the air is driven through tho valvcn V a 
into the reservoir bellows I), from, which the 
air passes to the organ. Tho pressure on l> 
depends on tho weight W on the top board. 
To ensure a uniform pressure in .1) whether it 
is expanded or contracted a double set of ribs 
is used, the upper set R, folding outwards 
and lower set ll a foldin" inwards ; tlio f ratlin 
H. between the two sets of ribs is connected 
by a mechanism shown so that both halves 
of the reservoir bellows expand equally. 

{22). At the opposite extreme of the typo 
is tho sqiieo'/cd rubber tubo pump (./''if/. IB) 0"). 
This pump consists of a rubber tube A,A| 
, '?ifj. 5) wrapped inside a hollow cylinder B and 
squeezed by two or 
more rollers 0, and 
so that tho way 
through tho tube is 
stopped nt tho 
squeezed portion. 
Tho rollers O l and A s 
Oj roll round the 
inside of tho cylinder 
driven by the shaft ^ 
1), and gas (or liquid) 
is transferred from 
A! to AS as the shaft 
revolves. 

Tho squeezed por- 
tions act us pistons, 
and these " pistons " 
arc formed at AI 
and travel along the tube to A 2 where they 
disappear. 

The action of the pump is somewhat similar 
to tho rotary pump of /% 10, with tho 
important di'ffercnw that tho " piston " uf 
the rotary pump requires to be carried across 
from A, 'to A L and is thus liable tn causo 
leakage "of air or liquid. Tho tube pump has 
no dead-space and is only limited in range by 
tho strength and tightness of tho rubber tnhn 
to resist the pressure difference ; hut its speed 
is small and mcdianiimlly it is inefficient. 
Tho tube pump 5s particularly mutable fm- 
transferring gasca or liquids without mm- 
lamination, as tho plain tubo can bo eamly 
cleaned and no other portion of tho pump 
can come into contact with the fluid being 
pumped. 

An ovon simpler pump of tho name type 
can clearly bo made out of a plain piece of 
rubber tubing pressed with tho fingers, 

Ad. liotari/ Pumps 

(23) BLOWERS.- Tn this class the variation 
of the volume of U is effected by tho rotary 
motion of solid bodies constituting part of itn 
walls. The pumps arc usually driven by 




AIR-PUMPS 



11 



(-1 are intended for continuous action ; 
Joto therefore- with, solid piston pumps 
tn with other types of Class A. Over 
m pumps they have the advantages 
-nical efficiency ; in incchanieal 
' and consequently in cost, both 
niicl for upkeep ; in e compactness ; 
noas of air current when used as 
They have disadvantage in a smaller 
liiTsauro, in greater leakage, and 
iti noisiness. But pumps of this 
i]iote also with those of Olass 1! 
V B(/)- M"' blowei-s typo lif/ 
1ms the advantage in mechanical 
ami simplicity. Ifor eompressnrs 
little to choose between Ity and 
though tho latter has tho greater 
th types would bo replaced by AH 
;ov range were required. l)'or evacu- 
1 is useless, while Ad provides the 
machines of modern practice for all 
between 10 mm. and -01 mm. 
Kief examples of the class can be 
into two groups, one (I) developed 
from the liocit Blower, the 
other (2) frnm the IJcaln 
Blower. Tho development 
lias been so gradual that it 
is difficult to associate any 
of tho pumps, or even the 
two archetypes, with the 
.. , name of any inventor. The 

groups are usually distill- 
:yy tho nature of the " abutment," that. 
iiio or siu-faeo dividing tho 1T.P.V. 
D 3'j.P.V. ; group (1) is then tslnirae. 
uy a movablo abutment, (2) by it 
ittmcnt; for though in (2) the bodies 
tho abutment move, tho lino or wir- 
es h is tho abutment is a.t rest relatively 



LE ABUTMENT. TllCSO pumps 
fly used for moving largo quantities 
against a small pressure difference 
to fi-10 feet water pressure). 
vly example of this typo was exhibited 
J?aris Exhibition hy Elilm Hoot in 
ff, 14), It consists of two two-tootlicti 
A, :ii, whioli are made to revolve at 
o rate in opposite directions by moans 
tmtsklo the box or pump hotly ; the 
iciludcd botwcon tho wheels ami tho 
is U, and its volume varies with tlm 
of tlio wheols. If they potato as 
11 the figure air would ho sucked in at 
eliverod through '!>. 
-ovent louUage tho wings .are muehined 
.trntely an jinssilile, and tiro often 
with wood or other packing material. 
ImnoU'ic oflleieiuiy against small press- 
ny 10 inolies of water) may bis as 
t Otl ]ior cent h vi'hile nt higher ])ress- 
ft-ct of water) it will drop to 80 pot- 



icnl. The over-nil mechanic-ill efiiciciioy is 
abimfc 7 per cent. 

Fty. It) shows another ly]io whero the 
imjidler vunes V are ffialc*iHHl (it one end to & 
disc whicsh Cannes them to rotate around the 
fixed core. The vanes nltrr the delivery 
sti-olto eomo intu the openings in llio rotating 
body A (called the id lor), which is canaccl to 
rotate at the same speed as tho vanca b 
on the outside. On rotat- 
ing further the vanes como 
into tho suetion chamber* 
whence they start again on 
the compression strolio. 

Tho pump is more com- 
plicated. than the Hoot, 
but several advantages arc 
claimed. Tluia surfaces 
ean bo used to separate- tho 




. If). 



two olinmbers whero lines only are possible 
in tho Hoot blower ; ait- is compressed by 
one rotating part only ; there is no contact 
between parts moving with different velocity, 
mid tlniH there is IOHH friction ; the mechanical 
construction is itii])le and cheap ; tho pulsa- 
tions of gas arc redueed. 

In another typo fhe rotating parts are 
npiral vaneff, which give a more even, delivery 
of {jus uiul makf] ICHH noises ; the mechanism 
in not .easily nlinwu in a diagram. Many 
(itiicr deviees liave been ui!ii])te(l, Rfimo vary- 
ing widely lit detnil from thosp mentioned, 
but all based on the samo principle ; descrip- 
tions o them are to bo found in maliera' 
ciitiilogncs. 

(25) Fix Kn AntiTMHNT. These! puni]iH, of 
which tho licalo blower in an early example-, 
are used extensively as compressors, aa blowers, 
and as ovaomttors. They are mcA in Rns- 
workH for 
pumping the 
gas: to the p 
holders, and - B 
in tho factory or 
laboratory for at- 
taining pressures 
down to -001 mm. 
Tho general prin- 
ciple employed is 
shown in Fitj. 10. 
Tho cylinder I) rotates alxnit anaxiHl),Bo lhat 
it'tonohos tho oontainhiK cylinder C ut tb fixed 
abutment 11. A Hint in 1> curries tlw llnlc 
or " sorapoi-H," the outer cuds of which ore held 
against tho containing cylinder C. Tho ptalcs 
divido th aiiacn Iwtweon and I) into two 
parts ; as 1) rotatPH the volumes of thcao two 
Itarta vary in n inannor readily ncen from tho 
fij^uro, in which P is tho auction imd Q tlio 
oomprMsion inlot. 

Tho friction of tlio snrapors on thu cylinder 
involves coiiHidorabb lows imd \ITIU-, and many 
alternative arrangcnienta have been devised 




12 



AIR-PUMPS 




bo avoid ife. In one, contact between tho 
scmpers ami tho cylinder in preserved by a 
emiular guide with its cenlro (joiiusident with 
that of 0. In another thorn is a single solid 
scraper which slides frcoly in tlio slot in 1) ; 
fcho section of tho oylindor 1) is not circular, 
but such tliat tlio two ends of tho semper 
aro in contact with tlio walla whatever the 
position of I). In another tho sonipors tiro 
pushed out by springs, but they boar on nil 
idly rotating cylinder (" litting closely within 
O nnd pierced with holes ; tho clearance 
between C' and 0' is inado no small that tho 
leakage between the two is inappreciable ; 
tho friction is thus reduced to that of 0' on 
its bearings. In any 
pump of this typo, tho 
number of scrapers may 
bo increased. Fig. 17 
shows a typo witli throe 
or nioro scrapers, hinged 
at tlio central axis M of 
J tho box IS, mid sliding 
FIG, 17. in cylindrical stuffing 

boxes fastened to tho 

rotating drum D j this drum touches tho 
easing in tho fixed abutment E. 

In pumps of this typo designed as ovaouators 
oil is always introduced into tlio cylinder to 
prevent leakage and to fill up the dead spueo, 
Tho scrapers aro usually arranged aa in Fig. Ifi. 
In order to prevent hammering by the oil 
when tho vacuum is high, a valve ia fitted 
which limits tho quantity of oil flowing from 
the compression side ; it also helps to sopamto 
the air from tho oil. Such ovaouators aro 
often run in tandem, or one of thorn is used in 
series with an auxiliary pump of some other 
kind. If pnh'i to 10 mm., p { , nmy be reduced 
to -0001 mm. 

Semper vacuum pumpa am largely used 
aa auxiliaries to high- vacuum pumps (C) ; 
they aro also tho cliiof typo employed in tho 
preliminary evacuation of electric incandescent 
lamps, which aro subsequently " clcaned-up " 
by tho discharge (D). 

]J. AKHOOYNAMIO PUMPS 

(2(i). In aerodynamical pumps, tlio proas- 
urofl aro functions of S and of tho velocity 
of the gas in different parts of tho appaiutiiH. 
Tho fundamental connection between tlio 
pressure and velocity of any fluid is given by 
tho familiar hydrodynamicat eq.un.tion 

%H-^ a )^0, . . . (24) 
or Pi- P = &(* -Vi*}. - - (2fi) 

It is deduced on the assumptions (1) that tho 
energy required to change the pressure of u 
volume Y of the gas from ^1 to p a is (p l - p^V, 
(2) that the energy of any such change of 
pressure which occurs is equal to the change 
in tho Idiiotic energy of tho gas. (1) implies 



that the fluid is incompressible, 1 or that Un' 
change in pressure is infinitely small ; (2) Lhivl^ 
there is no loss or gain of energy to or from 
other sources, c.y, friction of the moving gas. 
.By " tho pressure " must bo understood tlio 
force per unit area on a surface at rest relative 
to the gun ; in a frictionless fluid it is eqmil 
at any point to tho " static " pressure on ii> 
surface parallel to tho flow at that point, bill' 
moving relatively to tho gas ; tho " dynamic '* 
pressure, or that on a surface perpendicular 
to tho (low and at rest relative to tho pump, in 
p + lpv s , n,] id, when (24) is true, is constant 
along tha whole stream. 

lie. Injectors and Ejectors Qaaeaua Stwam 
{General Reference (11)) 

(27). Those are wholly analogous to liquid 
jot pumps (see "Hydraulics "). A gas or vapou r 
(called l< tho fluid " to distinguish it from the* 
gas to bo pumped) is forced through a tubes 
N from a reservoir 11, at pressure yt\\ t into a. 
larger tube communicating with the atnid- 
sphcro (aao Fig, 18). If tho How satisliml 
assumption (2) above, tho stream would nub 
bo brought to rest in tho atmosphere unlcnH 
p tt wore equal to II, and if jin = ll there woulil 
bo no stream. But owing to viscosity and 
friction, ?)]j may bo greater than II, so that u 
high volooity i>x is obtained in N, and yet 
may tic zero when tho atmosphere in reached. 
In these conditions, tho clifToronco 1 1 - p, whero 
p is tho pressure at N, is not HO great as Jpl'.v 3 
given by (24) ; 
but it is still 
finite nnd of tho 
same sign, j p is 
leas than. II. 

If ga-R in the 
space surround- 
ing N ia given 
across to tho 
stream through 
tlm gap between 

N and (I, it will flow into tho stream of fliiM 
and bo carried away by tho stream, BO lonj^ 
as its pressure is greater than p, Tho iluitl 
streaming from N to will suck gas throng] i 
the pipe (J and will aet as an ovacuator or 
" ejector. " In an " injector " or compressor, 
Q communicates with tho atmosphere, and thi* 
space with which communicates, and in 
which tho stream comes to rest, is at a proHBiim 
greater than II, but, of course, still much ICHH 
than pit- ]) is equal to p f f in an ojoctor and 
to p,, in ft compressor ; but if there in u 

1 OonfiiHlan IH somntlmca lulrndimert l>y n fnlliiro 
to observe Unit tho chief part of t!m nrcflsnro of u 
Kan IH iiiMopaml)ln from ItH comim-aslblllty ; It in 
not ilno, liko that o( a liquid, to its welffhl. Thu 
lircssure of tin Incompressiblo HIIS Is a nicnnliiRlmH 
(toiiceiitioji. Tho fliiplliifitlon of the theory to RaHC' 
Is jiistinccl only becnuap, for small ohaiiRca of iiressuro 
lit constant temperature, pdV = - Vilp. 




AIR-PUMPS 



o on tin iml stream of gas through the pump, 
pi, or PH will not lie equal to j>, (1) because of 
the drop duo to How of the connecting tubes 
(J and 0, (2) because tho mixing of Urn gas 
with tlio fluid affects greatly tlio velocity mid 
pressure of the latter. 

In calculating the performance of a pump, 
allowance has to bo mado for departures from 
(20) owing to friction and viscosity. The 
allowance ia usually made by introducing 
on the right hand of (25) an empirical factor 
f, less than 1, and writing 



where v lt v 2 are tlio mean velocities over a 
cross- section of tlio stream. The principle of 
the calculation is thon simple. There are throe 
equations (20) for tho tlirco tubes N",' 0, (J ; 
and there is the equation of conservation of 
mass when tho streams meet. (Tho momen- 
tum is not conserved, for thoro in a reaction 
on tho tubes.) Theso four equations suflieo 
to determine tho four unknowns, viz. p, %, 
uoi f<ji in terms of p\i, pj, t p\\, tlio densities 
p e and p f of tho gas and fluid, the throe 
empirical constants for tlio three tubes, fa, 
i'tit fa, and I (I N, fc\)t -l^q. t'bo cross -sections of 
the three tubes at their openings. Tho algebra 
need not be set out, for the numerical re- 
sults depend wholly on the values attributed 
to the empirical constants ; it in given in (11). 
Here it will suffice to state some of tho most 
important qualitative conclusion", which are 
confirmed by experiment, These wore first 
stated by Uoiinoi 1 (12). 

Tho variables considered are p\{, pi., pn, %, 
I^N. l ( 'o, I'V p a , />/. iwul 8, the volumetric 
speed, which is equal to Wqli'tj. In each 
statement tho variables not mentioned aro 
supposed constant. 

(1) P-Pi, is proportional to pn and %*, 
HO long as ]}[i in great compared with pu or p Sl . 

(2) 8 is proportional to \^pu, to UH, am! to 
1>\\ -'/>L subject to the same condition. 

(3) PnPi, depends only 011 tho ratio.i of 
tho i'"s, and not on their absolute values. 

(4) S is proportional to tho !?", if their 
ratios are constant. 

(fi) Given one of these ratios, there in an 
optimum value for the other two, giving 
maximum S, but the same 1 maximum S oan 
bo obtained with different values of tho ratios. 

(d) S is independent of p a and p fl so long as 
VH is constant. 

(7) S may bo considerably greater than the 
volume of fluid insuring nor second from N, 
e,g, two or three times as great. 

Owing to the niroiinistaiiecs in which the 
pumps are used, the efficiency is seldom 
important. But the mechanical ellicic.ncy 
reckoned on tlio basis of the work done in 
dr'.ving tho fluid stream appears fmldom, if 
o ir or, to exceed 2/i nor cent. 



g (28). fn practice tho fluid used ift generally 
strain or if((iii]ii'(.isscd air. Ejectors using tliRHo 
fluids are n.ied for vaeinun brakes, vacuum 
cleaners, and grain conveyers. Their great 
advantage) is, of course, their simplicity and 
freedom from maintenance charges, fig, 18 
shows a pump used for railway vacuum brake 
operation. It will rnduco ?>j, to about 15 orn, 
of mercury. A more elaborate pump is 
shown diagrainmatieally in Fig. 19. Hero a 




common supply of steam works two pumps 
in series. Tho lirat consists of the plain 
noM/.lo A, tho stiiiond in tho annular gap .11, 
from which the gas is carried into tho sur- 
rounding nnnnlar space ('. It is claimed that 
this pump will attain n pressure of 3 urn. ol 
morcury. Kemark Hhould lie iniido that tho 
a]i]ilication of the simple theory to sueh pumps 
in ' extremely precarious, for the assumption 
that tho change of proHsniro f the gas is 
infinitesimal is clearly [also. 

Fiff. UO showa a blower usort for moving 
largo quantities of air in ventilation under a 
pressure of a few 
inohea of wator. Air 
or steam ia used as 




Iluid ; tho ooncontric 

cones ore designed to 

make tho velocity of via. no. 

tlio gas Hourly parallel 

to that of the fluid, so thnt the dii'ectiim of How 

of the latter is not disturbed by irregularities 

in tho flow of tho former. A somewhat similar 

arrangement in adopted m the smoke-lmx of 

a locomotive, whore the exhaust steam is 

miulo to create IT, draught through the linilcr 

duos. 

(20). Tho most modern development of 
tlio typo is tho mercury vapour jot pnmp used 
in conjunction with " condensation " high- 
vacuum pumps ((/.!'.). Indeed, as will bo 
seen, the lino between vapour jot pumps and 
condensation pumps cannot bo drawn sharply ; 
roughly it may bo .sot at tho pressure where 
the mean free path of the vapour molecules 
becomes comparable with tho diincnniniiH ut the 



14 



AIR-PUMPS 



tulies ; but there is no justification for over- 
looking biio distinction entirely. Tho isonstruo- 
tion of these vapour jot pumps is essentially 
similar to yiij. 1.8, but the apparatus is made 
of glass ; the vapour stream ia producer! 
by boiling mercury, and confirming arrange- 
ments aro provided for returning tho vapour 
to tho [toiler, A practical form designed by 
Volmor (13) will reduce the pressure from 
Jin = 20 !"' () f mercury to jJi, = '001 mm. 
iiut it is doubtful whether they will replace 
generally the rotary aerostatic oil-pump for 
producing the axixiliary vacuum of high- 
vacuum pumps, Fragility is their great fault. 

B/. Injectors and Kjectors Liquid Slretun 

(30). This typo of pump, of whioh tho 
laboratory filter pump (ffitj. 2Li) is & common 
example, is often regarded ns a mere modifica- 
tion of .Be, gins or vapour being replaced by a 
liquid as fluid. Iiut tile difference is really 
great oi 1 . 1C tho theory of lift is applied to 
pumps with liquid as fluid, then, even iE all 
phuiMhlo corrections arc made, tho 
calculated pert win once is far lass 
{&.g. 10 times) than the actual. Tlio 
error arises in assuming that the 
gas and fluid are miseiWo. The 
flow of tho gaa into tlio fluid is not 
determined simply by the pressure- 
difference, and relative motion of 
tho fluid and .gas ia possible, ovon 
niter they aro mixed in the exit 
tube O. 

. 2lA. Ik sccina preferable to look ufc 
their action from a different point 
of vioic, TITO processes are involved : first, 
tlio entiuiglmg of thogtts Iiythe liquid stream; 
second, tho conveyance of the entangled gas 
from the LJ'.V. to the H.P.V. During the 
second jii-ncesa tho gaa will move relatively to 
thfi liquid nearly as if the lirjuid wove at rest 
i-cliiUvo to tho vfiMfi. The (lilVni-nnco of prossuro 
ultimately obtainalile is limited only by the 
condition that the velocity of thn Jiqiiif) ontcj-- 
ing tlioI/.P.y. Jy N is Buffioicnt to orry it 
ift tllpoiigh O flgatust tlio prcsstiro 'ji\i-jij., 
and is also greater tlnui the velonity with 
which tho buliblcs of entangled gfia travel 
Ihrough tlio liquid in tho opposite direction. 
It is tlin second process which determines! 
fch,o greatest possible value of .pjj -prf, 

On the utlior hand, the apoecl of tlio pump 
is detcrmincfl by tho first process. Its nature 
5s obsoiiro ; probftWy tlio )ir[tji(l stream carries 
along a layer of gas on its surface, in virtue of 
friction mid viscosity (of. (39)), aa would a 
solid rod travelling with tho stums velocity. 
When fcho liquid breaks into drops in virtue 
of the inherent instability of liquid jots, this 
gas beenmoB entangled between tho drops. 

On this view tho jwrfornmneu of a pump 
of this Typo appoiws quite incalculable. No 




2111. 



calculations confirmed by experiment scorn 
to have been based on any view, and few data 
of performance or of. its variation with the 
construction of tho pump seem available. 

(vJl). Tho filter pump of /'V.?. 2U fed with 
water at a head of BG ft, or more will reduce 
pi, ii> tlio vapour pressure of tho water. Jinfc 
ti<> measurements of 8 under varying conditions 
have been found, 1 1 is recorded that the, 
pump is more efficient if placed at tlio top 
of a building HO high that tho exit tube can 
bo made as long as the water 
barometer. 

A variant on the usual design 
is shown in Fig. 2 IB, which is 
similar in construction to the 
Vontiu'i meter. But sinco fclio 
notion is improved by a linffla 
at 6 which breaks up the stream, 
itia probable that, as suggested, 
the formation of drops in an important part of 
tlio process. A imn-roturn valve, as shown at 
V, is tiscful with cither of thcHO types to 
prevent the How of water into the apparatus 
if fcho head becomes insnfllek-nt, 

JUwiouatora of these tyjics nro applied 
outside tlio laboratory to vacuum cleaning 
anil to grain conveyors, Compressors work- 
ing on tho same principle, but with a difl'oront 
construction, havo also important (lommoroial 
lines ; they aro known as " brompes," In a 
very simple form (fig. 22), used for blowing 
blacksmiths 1 fires, a stream 
of water flowing tlowji a 
pipo with 11 low holes in it 
drags with it ir from tho 
atmosphere, wliiali is fldlj- 
eequoniiy separated from 
tho water in a closed vessel. 
A more elaborate form has 
hccm developed in America 
for mipplying (iiinijtrcased 
air to mines whero a great 
hojwl uf wnicr is availftl>lo, 
Tlio pressiti'o o)>taii)blo 
i o eonsidorablo frnetioa 
nt tliat cm-ri-'spomling to 
water. 




. aa, 
tho head of tlio 



umpn 
(General Koforrmco (II) and (14)) 

(32). Centrifugal air-pumps are analogous 
toeonLrifi'gallin_nid.pnmps(seo "Hydraulics"), 
They nrn gcnoi'nlly callod " fans," fttid urn 
used as lttnn or blowers according to the 
definition of tho introduction. Tlio principles 
is shown in Fig. . 23, which illustrates the 
simplest typo. Tho gna ontormg the eiroiilar 
central aportnvo in tho housing is whirled 
round by the rotating vanes, acquires velocity* 
and inso8 through Ii. 

Suppose that tho conditions neco88a,yy /or 
(24) aro fulfilled, and that tJio gA9 loaves t),o 



AIR-PUMPS 



15 




tipsVTho vanes with a HM volooity J, 
uniform over tho whole surface of the oirculai 
oylindor surrounding the vanes, llw area 
of this surface is Zllrf^i, whore r m tl w 
radius of the vanes and d their l)readth poi- 
pendicular to the diagram. Then 

s=li . liv . . . (27) 

If F a is tho area of the opening, and i- a is tho 
velocity of exit uniform over tho opening, 

/oo\ 

G "17 ?) . - \*-"/ 

If the gas in acquiring its velocity from the 
vanes preserves its original pressure p ta tlion 
from (2fi) 

p -3, 4 =ip(V-"a')=i' jSa (ir*"F")' (29) 

But, as in Section He, (24) is not true and 
allowance has to he made for losses of energy 
duo to friction and to sudden 
changes in the direction of 
tho gas stream. Further, the 
velocities are not uniform Over 
the surfaces l!\ and liV Again, 
it is convenient to express 
PH-PL '""I & Ul terms of tho 
velocity of tho vanes which can 
1>o measured directly ; it is usual to represent 
this velocity hy v a , tho linear velocity of the 
tips. It may ho assumed that v v and v are 
proportional' to i' n . Tho losses may bo then 
represented by one or more terms proportional 
to v\ or to S ! | or to Sv , and tho gonoral equa- 
tion for tho performance of tho pump written 
,, _ (U , o 2.|.p ? , Q S + . v Ra. (30) 

The constants a, 0, 7 are usually regarded 
as depending on the angles at which tho 
stream of gas strikes tho vanes and tho 
housing ; they certainly depend on tho 
geometrical quantities characteristic of tho 
pump. Some progress towards calculating 
thorn directly from those magnitudes can bo 
made, but some purely empirical constants 
are always necessary. In designing the forms 
of the vanes and of tho housing such calcula- 
tions arc a useful guide ; here reference can 
only bo made to discussions in (11) and (Id). 
It may ho noted that in (80), a is always, p 
usually, positive, while 7 is negative. 

Three kinds of efficiency are recognised for 
centrifugal pumps : 

g (;);}}__(!.) '.['lie inanomotrio efficiency T!,,,,,,,. 
is taken as (j) H -?)i,)/p a ,?>i, (usually If) and p n 
being tho static pressures of tho inflowing 
and outflowing gas. If ))-, were equal to , 
tho maximum value of IC|, I!H1 . would bo -J-, 
but since w, may bo either greater or ICHS than 
. I'-TILUI, might theoretically have any value ; 
actually it is soldom if over greater than I . 

(ii.) The mechanical oflii'.ionoy ]<!,,,[,., The 
useful work is generally taken to ho given by 



(0), HO that if w is tho power exerted at tho 
pump shaft, 'K, uw \,. = &(pn~l'>j l )lw. Some- 
times tho useful work is reckoned hy ())), 
tho corresponding efficiency is called tho 
total efficiency, hut it is seldom important, 
as previously explained. ~K, uce ^. IK a true 
efficiency and can never he greater than 1. 

(iii.) Tho volumetric efficiency K^,, which 
is taken hy some writers to bo S/ty 2 ftn( l by 
others to bo S/Z-n-rdv u . The latter quantity 
would bo unity if J\ were equal to v ; tho 
former seems to have no general significance, 
hut, being a no-dimensional magnitude, is 
convenient for comparing similar designs. 
E vn i. is often greater than 1 if tho first 
expression is chosen, sometimes if the latter 
is chosen. 

It is apparent from (30) that tho pressure 
and tho efficiencies will vary with S, if S is 
controlled hy changes in the area V 2 m hy 
other changes in tho resistance to tho flow 
of tho gas. Fig. 24 shows typical curves 
relating tho brake H,P. w, tho pressure clif- 
fcroneo p^-pi,, and tho mechanical efficiency 
to the volumetric speed S, the velocity of tho 
vanes heing constant, It will bo observed 
that HUM efficiency is oro for S~0 and for 
high values of R and has a maximum for some 
intermediate value. If mechanical efficiency 
is required tho pump must be designed for its 
special work. If the velocity of tho pump is 
varied over a moderate range, S varies as 




Vj, Pn-pr, its v a > and tho power expended is 
". For extreme varieties tho " constants " 

of (HO) change. 

(;!4). Simple centrifugal fans differ in sr/.o, 
in 'the number and shape of the vanos, and in 
the shape of the housing surrounding them. 
This is often divideil into a "diffuser," or 
portion with parallel sides immediately out- 
sido tfie vanes and a "volute," or portion 
of circular section, outside the diffuser. Tho 
cross-section of tho volute increases towards 
tho outlet in order to make some use of tho 
kinotie energy (see ()) Somo fans have 
inlot openings on both sides of tho fan, some 
only on one. JUit in their performance, 
they all have common characteristics ; they 
are' all used as low -pressure blowers, the 
maximum pressure obtained being about 12 m. 



16 



AIR-PUMPS 



of water ; palpi, does not exceed 1-03, and 
assumption (1) of (28) is J^tihe, . In 
large sizes their mechanical efficiency may 
reach 80 per cent, but usually it is more nearly 
70 iier cent and intermediate between that 
of piston pumps and of Root's Blowers. Over 
cither of these types they have the advantage 
of simplicity and of being proof against hot 
and diisty gases if the bearings arc suitably 

Prf Composite, or multi-stage, centrifugal fans 
are also common. The fans of successive 
stages run on the same shaft ; the discharge 
from tho circumference of one fan is led by a 
tube to tho central intake of tho next. Since 
- Pi is proportional to p by (25) and p is 
proportional to p,. or p a ,vn have in successive 

stages Sp'p, or PJPi-*"',?. K 1S , 1G 
range of the simple pump and is the, number 
of stages The range of the composite pump 
is the" product of the ratio-ranges of the . 
individual stages. Such multi-stage fans with 
ten or more stages, each giving * = 1-1 when 
driven by a turbine or electric motor at 4000 

r.p.m., are 
used to deliver 
ail 1 to blast 
furnaces at a 
pressure of 2-J- 
. atmoa. They 
are also used 
for " Kiipor- 
charging" 
petrol motors 
on aeroplanes. 
In Fiij. 2fl a 
3-stege fan of this kind is shown ; details of 
bearings, rings to prevent leakage, and the 
water-jacket of the outer casing have been 
omitted. A, B, C are the revolving " im- 
pellers," while tlio parts drawn solid are fixed. 
Bateau constructed a simple fan, running 
at 20,000 r.p.m., which gave = 1'6; experi- 
ments on extremely high speeds have also 
been made by Parsons and others. But 
such simple fans seem to have no practical 
advantage over the composite type. 

B/i. Airscrews 

(General References (11) and (14)) 
g (35). In type %, the velocity of tho gas 
produced by a" rotating solid is perpendicular 
to the axis of rotation ; if tho velocity is 
mainly parallel to that axis, tho fan may 
bo called a " propeller," or, better, airscrew. 
In all that concerns tho general relations 
between tho velocity of the solid and tho 
velocity or pressure of the gas, airscrews 
are indistinguishable from centrifugal pumps. 
Tims tho pressure produced by an airscrew 
is proportional to the square of its velocity, 
the volumetric speed to tho velocity, and tho 




power to the cube of the velocity, (:U>) i 
still true, at least approximately, and wimiliii'ly 
defined efficiencies might be employed to stiilo 
the performance. 

The difference between airscrews and 
centrifugals lies in tho connection bctw^n 
the constants of these equations and fch 
geometrical magnitudes. Much more is known 
of this connection for airscrews, perhaps on 
.account of their im- 
portance for other pur- "'- ,n Ss" 

poses; for this know- ' " Mt ' ^ '- * 

ledge reference may 
bo mado to " Aero- 
dynamics"; since tfio. 20. 
airscrew pumps are 



ow 
Jn 



tbLIOULUll |_Fiim_|- |< 

not very important, no further account >i 
their theory need bo given bore. 

(36). Airsorows are largely used for venM- 
totion, either stirring up the air in a room Mi- 
extracting it into the atmosphere through u 
hole in the wall. A plain wi-wii-ov is visry 
inefficient for tlio second purpuw, since th 
difference of velocity between the centre iul 
circumference of tho screw produces a cLrmilii- 
tion within the fan itself, as shown in Intf. ^ 
The loss' due to this circulation is greater wlmn, 
as in Fiq. 26, it is the H.l'.V. that is partially 
closed than when it is the L.F.V. To nlm- 
the loss the centre of the airscrew is ofbnii 
covered with a disc to prevent the rotum 
flow; the volumetric spued for a 
diameter and velocity is tlmrobj 
but tho mechanical efficiency in increased. 
It is impossible to secure that all the en 
given to the gas shall produce axial f 

some inefficient tangential find radial 

is always produced at tlio same tune. 

tho Ratoau scrow fan, shown in Fig. 27, tlio 

tangential and radial flow 
^sgreatly reduced by causing 

the gas 'bo strike the blades 

(B) with a velocity opposite 

to that of their rotation. 

This velocity is imposed 

on the inflowing- gas by the 

fixed vanes V. The centre 

of the blades is covered by 

the fixed disc T>. ft shows 

u transverse sec I; ion through 

the fan, b a " cylindrical " 

section made by a cylinder 

coaxial with tho fan , cutting 

15 and V and developed into 

a plane. In 6 the motion of 

the blades B is upwards. The Katean wvrow 

fan resembles in its performance a Himplo 

centrifugal. 

Some fans, described as of " mixed flow," 
aro intermediate between centrifugal am) 

airscrews, tho flow of gas boing partly nulial 

or tangential and partly axial. lint they <ln 

not differ sufficiently in principle from the 




AIR-PUMPS 



17 



many fcypos of pure airserows and centrifugals, 
wlticli are also described in makers' catalogues, 
to warrant special notice. .For small powers 
there Booms little to choose between these 
classes of fans ; for larger powers the contri- 
ftigal is more suitable ; it is also more suitable 
for the individual members of a composite 
pump. 

Ri. Thermal Pumps 

(37). The principle of those is sufficiently 
dismissed under "Convection." The chimney 
of the open fire which ventilates a room and 
tlio gas jet in the fluo of tlio chemical fume 
cupboard are familiar examples of " blowers " 
of this typo. The draught produced by a 
flame in a fluo has also boon used to work 
small wind channels for aeronautical investiga- 
tion. ; and generally, if only very small powers 
are concerned and efficiency is unimportant, 
chimneys and small fans may bo regarded as 
mutually interchangeable. 

C. HlOH-VAOUUM PUMl'8 
(General Refenmocs (21), (23)) 

(\}S). During this last few years pumps 
1m vo been invented which will attain pressures 
doliiiifcoly lower than those that can bo reached 
with any of the pumps described so far. They 
dopcmd upon " molecular " processes, that is 
to say, processes explicable by molecular 
theory and not by hydrostatic or hydro- 
dynamical theories, which regard a gas as iv 
continuous medium. These processes become 
important only when the pressure of tlio gas ia 
boknv some dolinito limit, which is usually far 
liiilow that of the atmosphere. Tlio puinps 
must therefore bn run in sorios with an 
auxiliary pump .whioh roduoos and maintains 
tUo pressure below tlio limit at which tho 
notion of the molecular pump begins ; this 
pressure is of the order of 0- 1 mm. As 
auxiliary pumps, those of typo (Ad) are now 
usually employed. Further, since the vapour 
pressure of water in much above the limiting 
pressure, a drying agent must bo used in 
conjunction with the auxiliary pump ; on 
the other hand, a molecular pump does not 
distinguish between vapours and permanent 
gases, and no device is needed to remove 
from the low- pressure side of the pump any 
vapours except those whioh arise from tho 
tic Lion of tho pump itself, i 

Two molecular processes have been employed ; 
for mush pumps, both originally suggested by 
Gaodo. Kinc.n the lirst typo was tlio only 
mombor of its clans when first invented, it 
wtis milled by its inventor the " molecular 
iininp," U is convenient to retain the term 
and confine it to tliis type, although tho 
(second typo, invented later, has an equal 
right to it. 
VOL. I 



C/. Friction Pitnijis 

(30) GAKOB MOLECULAR Pump. The 
action depends upon tho forces between a 
gas and a solid (or liquid) aiirfaeo moving 
relatively to it, At ordinary pressures these 
forces are determined by tho viscosity of the 
gas, and the influence of the solid boundary 
enters into tlio calculation of tho flow only 
through the assumption that v n , tlio velocity 
of the gas at that boundary, is zero and that 
there is no "slip." But at sufficiently low 
pressures Kuiiclt and Warburg (15), continued 
by many later observers, showed that the 
measured (low agreed with that predicted 
liydrodynamically only if it was assumed Unit 
there is Home slip, that v v , the velocity of tlio 
gas at the boundary and parallel to it, is 
finite, and that tho force exerted on tho gas 
by tlio boundary is cv u , t is called the friction 
coefficient and e/i; the coefficient of slip. 

From the molecular standpoint the matter 
appears somewhat differently. Tho condition 
i> = menus that the velocities of tlio mole- 
cules leaving tlio boundary are symmetrical 
on either aide of tlici normal!. The aj Clearance 
of slip at low pressure's dues not mean thai this 
condition is no longer fulfilled. l'r if the 
pressure is greater on one side of the normal 
than on the other, more molecules will arrive 
at Iho boundary from the first sido ; if the 
molecules leave tlic boundary equally dis- 
tributed on both sides, then there will be on 
tlio whole* a flow of gan from the first side to 
tho second, so long as the distance travelled 
by tho molecules leaving tho boundary before 
they oollido ia finite. On bho other hand, the 
flow will bo lesHs than it would bo if tha mole- 
culcs left tho boundary with their velocity 
parallel to it unchanged. Accordingly the 
condition v n ~0 is not inconsistent nt low 
prosHiires with the hydrodynamical assumption 
of a finite slip coefficient. 

Knudsen (10) hus calculated tho friction 
coefficient from such a molecular theory. Tic 
assumes that whatever tho direction of the 
incident molecules, the mini tier with any 
velocity leaving tho boundary within a cone 
of solid angle ilia malting an angle II with the 
normal is proportional to eon Cdu and tliat Iho 
distribution of velocities in Max well iail. Ho 
concludes that e--=e u .ji, where 



and p is tho density of the gas at unit pressure 
and tho prevalent twmporaturo. (,'tl) has been 
confirmed by experiments at pressures less 
than 0-001 mm. Gnodo (17) has shown that 
at higher pressures <? is greater, probably 
owing to the presence of a gas film on tho 
bounding surface. 

Consider a layer of gas between two infinite 

U 



AIR-PUMPS 



parallel plates, distant li from each other, 
moving relatively tn tho gn-s with velocities 
i, 2 . Let j) } , j) 2 bo tho pressures of tho gas 
at points distant L along tho direction of 
motion. TC tho pressure is HO high that the 
moan free path is small compared with the 
distance between the platca, tho forces on tho 
gas nro due to its viscosity ; tho relation 
between ;>, mid p a is given by the equation 
similar to that of Poissoiiillo ; 



6i, 



(32) 



But if the distance between tho plates is 
small compared _\vith tho mean free path, 
tho conception of n viscosity depending on 
collisions between molecules becomes in- 
significant, and tho equation must involvo 
only f, depending on collisions M-itli tho walls. 
It is fouwl tlmt 

log.^ = 5H 1 + a ). . . (33) 
Pi K 

Tho ratios of the pressures at opposite ends 
of tho plafcos is n function of tho velocities 
and of the geometrical quantities : it is in- 
dependent of the pressures, If any geometri- 
cal iU-TftilgiMnent other than that of parallel 
plates is used, this proposition is still true, 
so long as tho pressure is sumciioutly low, 
and so long as tho volocitica are consider- 
ably less than the mean voloeity of the 
molecules, Jf this last condition WTO not 
fulfilled tho distribution of velocities among 
tho molecules Jonving Hie boundary would bo 
no longer Maxirolliftn, and f would bo greater 
which troiild elefti'h/ bo desirable for tho 
purpose in viaw. 

(-10). Tito construction of Onedo's ])uinp 
(18) in- which this principle is applied is shown 
(Hug ram in aticif illy liy transverse) arid longi- 
tudinal sections in fig, 28. A is a cylinder 




FIG. 28, 

rotating in (.lie closely fitting housing B ; in 
the surface of A arc cut grooves into which 
project the obstructions attached to the 
housing ; tiio pipes and m open into the 
grooves on either side of C. If A rotates 
clockwise tho friction between tho rotating 
cylinder and tho gas lowers tho pressure at 
n and increases it at m. The grooves are in 
series from tho middle outwards ; m of the 
middle groove is connected to n O f each 
o the grooves on either Hide, and so on ; 
i of tho outermost grooves ore connected 



to the auxiliary vacuum (H.P.V.) and n of tho 
middle groove to the L.l'.V. A IN run at 
about 140 revs, per aco, by a pulley and 
motor. The axle passes through an oil box 
which seals the interior of the housing from 
tho atmosphere. The intrusion of oil from 
tho oil box is prevented by an Archimedean 
screw out on the axle, which driven tho oil 
bftukwnj'd ; tin's arrangement makes it of 
gmit importances that tlio auxiliary vacuum 
should bo turned mi after the pump if) star-tod, 
and turned off before ifc stops, 

Tho precise cnloiilfttion of tho pressni'CH 
obtained IB very complicated ; for there 3ms 
to bo taken into account, besides the driving 
of tho gag from n to m by tho friction of tti 
rotating cylinder, tho leak of tho gua fiaqk 
from m to n past tho obstruction C and over 
tho surface of the- cylinder between aiiciicHHivo 
grooves. But theory shows and oxporimcmt 
confirms that at a sufficiently low preflmmi 
tho ratio of initial and final pressures in 
proportional to tho speed of rotation and 
independent of the pressure, hut tho rntin 
falls off when tho pressure in any part of tiio 
pump vises above that (about 0-02 mm.) nt 
which 6 is equal to tho moan fvco path. At 
a speed of MO rovs. per sec. and an auxiliary 
vacuum of (H mm. pujpj, is about 1() D , HO 
that a pressure of 10~ mm. can ho obtained. 
But the ratio varies with tho gas, in virtuo 
of tho occurrence of p g in (III) ; it is less wiUi 
hydrogen than with air; probably hydrngon 



fj BOO 




formed a large part of the gas with which thin 
measurement was obtained. Lower prmmir^H 
could l)o obtained with a bettor fuixitinry 
vacuum ; but tho viwiuum attainable IB doll- 
nitoly limited by that of tho auxiliary pinnp. 

An important feature of these pumps IH i,Uo 
groat speed of pumping. Fig, 20 A shown H 
(in cm. 3 /see.) plotted against tho pimsm-n 
(log. scale) ; for comparison, TA abowa K Tni- 
tho Gaedo rotary movoury pump (Ah), 

Tho molecular pump would have wailo 
possible modern high-vaouum woi-It ; hut Jill 
its advantages, except ono, ai'o possomofj 
by tbci next typo of pin|> to bo oonaJilPiw'l. 
This one advantage is ihak it will remove tl 



AIR-PUMPS 



19 



vapours, while all other high-vacuum pumps 
leave morcury vapour, whioli has to be removed 
by condensation. But the advantage ia of 
iittlo practical importance for most work 
since tlio pump will maintain the vacuum 
only while it ia running ; if it ia to bo stopped 
and tho vacuum preserved, some form of tap 
or trap must ho inserted, and such devices 
always introduce vapours. On the other 
hand tho molecular pump ia necessarily 
expensive- and requires skilled attention. 
Despite its novelty ami ingenuity it ia already 
practically obsolete. 

('k. Diffusion 1'umps 

(41 ) DIFFUSION PUMPS. In Fig. 30 () lot 
H bo tho 1T.P.V. in which is maintained 
a constant pressure, L tho L.I'.V. to 1m 
evacuated. .List X ho a vessel in which some 
liquid can bo boated, while II, but not L, 
is cooled so as to condense its vapour. If 
tho liquid is heated to a temperature at 
whioli its vapour pressure P is largo compared 
with p n , a continual stream of vapour will 
pour along the tube XMH, driving tho gas 
before it and condensing in IT ; if the stream 




is sufficiently rapid tho gas in II will bo un- 
able to diffuse back into tho tube against it. 
On tho other hand, tho gas in L will diffuse 
out into tho vapour stream and bo carried 
by it into H. For this diffusion is not opposed 
by a vigorous stream in tho contrary direction ; 
since L is not cooled, tho vapour will not 
condense in L, and vapour will enter it only 
at a rate suflioiont to replace tho gas diffusing 
out. Accordingly, after some time L will bo 
completely evacuated of gas and contain 
only vapour. If L is now cooled, tho vapour 
will oondonso and an almost perfect vacuum 
bo loft in L. Tho vacuum will not bo quito 
perfect because Homo gas from H will diffuse 
back against the stream of vapour, however 
low is jj|[ and however rapid tho stream ; but 
a consideration of tho magnitudes involved, 
wilt show that. tho residual pressure could 
easily bo made inappreciable. 

Such in the principle of the diffusion pump 
in its simplest and ideal form. In practice- 
it is impossible ti> maintain the wholo of L 
{tho apparatus to he evacuated) at or ahova 
tho temperature of tho boiling liquid during 
the evacuation. L as well as IL is cooled 
sufliciontly to condense the vapour, and 
consequently if tho simple arrangement of 



Fig, 30 (a) worn adopted, tho diffusion of gas 
out of .L would ho opposed by a vigorous 
stream of vapour entering ; if the gas from H 
could not diffuse against tlio stream neither 
could tho gas from L ; there would bo no 
pumping. Some dovine, therefore, must be 
adopted to prevent a stream of vapour 
entering L. 

(42) GAEDE DIFFUSION PUMP, The device 
originally adopted by Gacdo (1!)) was to 
place in the tube loading to L an obstruction 
with a, very small opening. If tlio linear 
dimensions of this opening are small compared 
with the mean free path of tho molecules, tho 
laws of tho flow of gas and vapour through 
tho opening are not those of liydroclynamical 
atroaming, but those of diffusion. Tho flow 
depends on the partial pressure of the con- 
stituents of the mixture and not on their total 
pressure. Since , the partial pressure of tlio 
gus in tho tube XMH is zero, tlio gas will 
diffuse oufc through tho entering vapour in 
spite of the fact that tho total pressure of tlio 
vapour is greater in tho tube than in L. 
The problem can bo treated exactly by 
molecular theory. If d is tlio diameter and <r 
thc aroa of tlio opening at M, A tho mutui fi'to 
path, p tho density of the gas at a piTHHiiro 
of 1 dyne per em.*, then tho volume of the gas, 
measured at j>i., issuing through JI par see. is 
given by 

B = a- 7 _- f . . . (34) 

Vttrptt 
whore 



a attains the maximum 1 when <lj\ is mnall ; 
but o- decreases with d, Tlio maximum value 
of S, when A is lixod, is given approximately 
Ijy <Z = \. This maximum will increase with 
\, which, since tho vapour pressure nf tho 
liquid muat bo greater than p lt , in limited 
by pn. Accordingly tlio speed of the pump 
depends greatly on tho auxiliary vacuum, 
and also on tho tomporaturo of the liquid. 
For if P is too amall, gas will (M'unn biusk 
from H ; if it is too largo, tho dillnsion of 
gas from L will l>o lihidernd liy Lho onpuH- 
ing flow. Tho conditions in tho pump nocil 
therefore careful adjustment- On tho other 
hand, S is independent of tho ^IVCHBUIO oE tho 
gas and dependent only on its nature and 
tomporaturo i this ia tho most striking feature 
of all diffusion pumps. K in Creator for Lho 
lighter gases ; tho variation of >S with tho 
nature of tho gas is tho contrary of that for 
tho molecular pump. 

(<I3). Any liquid oould bo used in a, dif- 
fusion pump, HO long as it could be miuntuined 
at tho appropriate temperature. Actually 
mercury is used, for the appropriate tempera- 
turo is convenient (P^O-U mm. nl. HH)" (1.) ; 



20 



AIR-PUMPS 



moreover it is chemically stable and does nob 
mst glass. But its universal adoption is prob- 
ably duo in part, to the previous association of 
mercury with air-pumps an association based 
on quite different properties. 

The vapour of tho liquid used in the pump 
nt tlio pressure cm-responding to atmospheric 
temperature is left by tlio pump in L. It is 
easily removed from tho apparatus connected 
to Jj'by making the connection through a trap 
cooled' in liquid air. Tho introduction of tho 
cooled trap involves, of course, a continual 
stream of vapour opposing the diffusion of tho 
g!ia through L ; but at atmospheric, tempera- 
tures tho vapour pressure of mercury is so 
low that tho consequent diminution in tho 
spend of the pump is inappreciable. However, 
Gaedo (19) hits pointed out tliafc tho existence 
o this stream causes n slight error, appreciable 
ab tho lowest pressures, in tho measurement 
of tho pressure in Ij by a MoLood gauge. 
Since vapour ia streaming from the gauge to 
L, tho pressure of the gas in L is slightly higher 
than its pressure in the gauge. 

(44). The original diffusion pump of Gactlo 
involved complicated glass construction : since 
it, is no longer used, it need not bo shown. 
The maximum value of S obtainable was about 
80 em. and far below that of tho molecular 
pump at tlio higher pressures. On the other 
hand S was, as theory predicts, independent 
of the pressure down to tho limits of measure- 
ment ; at pressures loss than l()- ffl mm. tho 
diffusion was as good ns tho molecular pump, 
and no practical limit to tho pressure was set 
by tho diffusion of gas from 11 against tho 
vapour stream. 

Moreover, ib should bo observed that there 
is nothing in tho principle of tho pump to 
Ihnib its use to very low pressures, except tho 
condition tliab d = \ : if openings as small as 
tho free path could bo obtained at atmospheric 
pressure the pump would work. Gaodo lias 
actually used the pump at atmospheric pressure, 
taking tho pouea of an earthenware pot as tho 
openings and steam as the vapour ; but since 
the pores aro hacked by very fine tubes, 
through which tho gas has to flow hofore it 
arrives at tho pump, tho speed of snoh a 
pump is very slow ; it is not generally of 
praetioal use. 

(40) LAHOMUIH " CONDENSATION " PCMI-. 
A simpler and more efficacious method of 
preventing tho flow of vapour into L is to use 
the inertia of tho stream to carry it past the 
opening. Thus in the modification shown in 
Fig. 30 (/>), if tho velocity of tho stream of 
vapour issuing at is as groat as the velocity 
of tlio moletmlcs in the stream, all tho vapour 
will travel forward till it meets tho walls, of 
tho outer tube or the gas in H ; none will 
stream towards L and prevent tho diffusion 
' of gas fi'om TJ, although the pressure in tho 



vapour stream, as measured by its density, 
may bo very much greater than tho presauro 
in L. (It will bo seen that tho construction 
is similar to tho gas injector pump Be, 
but the principle of- action fo different. Tho 
gas from L diffuses against tho hydrostatic 
pressure ; it does not flow with it.) 

If tho walls of tho outer tubo wore heated by 
the vapour, tho liquid condensing on them 
would have a vapour pressure greater than 
that in L ; there would bo a (low of vapour 
from tho heated walls towards L, whicli is 
cool, and this stream would once more hindei 
tho diffusion' of giia from L. Accordingly 
Langmuir (20), who first used tins arrange- 
ment, laid great stress upon the cooling o1 
tho walls struck by tho vapour stream ; lit 
insisted that the vapour must ho immediately 
condensed to the temperature prevailing ir 
L, so that there should he no flow of tho vopom 
back towards L. On account of tho import 
anco attributed to this condensation, ho tormet 
his pump a "condensation" pump to distill 
guish it from Gacdo's diffusion pump ; but i 
is equally a diffusion pump in tho senso tha 
tho gas from L follows tho gradient of parthi 
pressure, not that of total pressure. Gehrt 
(21) has pointed out that Langmuir's prinoipl 
was anticipated by Magnus (22), who did no 
sco its applications. 

It appears, moreover, that though tho vor; 
efficient cooling of tho walls ami tho complot 
condensation is necessary to tho most oflicion 
working of tho pump, it is possible to make 
pump of this typo with much less oflioien 
cooling. This is achieved in Omvford' 
parallel jot pump (24). But in its worldn 
characteristics this pump resembles tho di. 
fusion rather than tlio condensation pumj 
and has not tho advantages of Langmuir 
pump noted below. 

S (46). The construction of Langmuir 
pump in metal (20) is shown in Fig. !H ; it en 
also bo made without great complication i 
glass (20). Tho mercury M is maintained at; 
toniporatiiro of about 100 0. by tho expend 
turo of about 300 watts, supplied eloctricall 
or l>y a burner. Tho baffle B deflects tl 
vapour stream downwards and against tl 
walls cooled by tho water jacket <T, Tl 
L.P.V. ia connected to L; tho auxiliai 
pump to H. If this pump nrnm.tn.ins 
pressure p a of O'Ol mm. or less, S in an gi'tt. 
as 3000-4000 cm. 3 /sco. and is, as btrfnro, i: 
dependent of p tl down to tho lowest obsor 
able pressures. Higher pressures pn clecrea 
tho speed, but tho pump will work oven 
tho pressure is nearly 0-1 mm. Tho spo'i 
is independent of tlio temperature of t 
mercury, so long as this is abovo a lim 
which is greater tho greater is p a . Tho gre 
speed of the pumpgreater even than t 
maximum of the molecular pump and t 



AIR-PUMPS 



absence of any need for the accurate control 
of temperature, arc tlio advantages that have 
caused condensation pumps to replace wholly 
tho original Gaodo type. 

Many variations on tho original Langmuir 
design have been made. Tn some of thorn 




If Hi, 31. 

(2(1, 27) tho heating of the mercury is effected 
hy an are maintained between two mercury 
surfatics inside tho ])uiii]> ; in fact ihia 
arrangement lias boon applied to large 
mercury- vapour current rcotifio.ra (28), an 
that the rectifier acts as its own high-viiciiuni 
pump, only an auxiliary pump being needed. 
Again, it has boon proponed (2i), 30, 31) to 
combine in the same- apparatus a mercury- 
vapour jet pump and a condensation pump, 
using the same stream of meroury vapour. 
Tlio two act in series, and the combination 
will work with an auxiliary vacuum of 10-20 
mm. ; but tho construction SB complicated. 

However, special reference need be made 
only to one typo of this pump, remarkable for 
its simplicity. It is found possible to dispense 
altogether with the inner tube in Pig. 30 (b) 
and to make the arrangement of Fig, 30 (a) 
act as a condensation pump by merely cooling 
the walls of tho horizontal tube. Since the 
mercury molecules striking tho cooled walls 
tlo not rebound therefrom, if tho cooled tube 
is 'made suflieiontly long, all the molecules 
emerging from its end at M will bo moving 
parallel to tho length of the tube and will 
not outer tho side tube. One form of such a 
jiump is described in (32). An oven simpler 
construction is shown in Fig, 32 adopted, tho 
whole being made of sheet metal. The limit 
iif 2 J u at which tho pump will work is about 
0-015 mm., and somewhat higher than that 
for the Langmuir type. Hut tho value at 
which tho maximum speed is obtained is not 
very different ; this maximum is about 1500 



cm. 3 /seo., and is sot by Lho dimoiimnr ..... f 
inlet tube" (sen below) rather than l, v 
pump itself. Tho auxiliary vacuum i.l I 
mm. for this or tho Liingmuir pump nm 
obtained by oil -pumps, and jnv:n<iii < 
difficulty. The simple pump of /ify. ;i;', 
well as tho Langmuir and other nii>n> .,. 
plicated pumps, is used on the lining 
scale in tho manufacture of lilninnioii.ii' \n\<. 
and other high-vacuum devices. 

(47) ITroii-vAODUM TECHNKJUI':. li, | ( 
been pointed out that fchcro miiHl. bit nu 
limit to tlio pressure reached by a ilihu.i. 
or condensation pump, determined by /'it " 
tho speed of the vapour stream. Win u 
high -vacuum pump is usud Lho |iiv i n 
attainable and tho speed of piim|>ini? , 
actually limited by factors other (<hnu il 
clliciency of the pump. In tho lln.i, ( U, 
the tubes connecting the pump to tho a|>| mi ,ii 
offer a resistance to tho How of JJRH. Kmnj: . 
(10) has shown that tho volumetric) HJH <>i| ..| 
pcifcct pump is given by 



where H is a coiiHtant dojiendciil. nf I In- I- 
of the connecting tube and /> w llu- dm 




FIG. 32. 

of tho gas at a pressure of 1 clviir/fiii.' 1 *, I 
a cylindrical tube of radius r and icujidi 1., 

*='&&- ' " 

If r is expressed in millimetres, I, in m< n. 
then for air at 20", 



S ia 1000 cm, a /sco. for air (loiviug 
tube 1 metro long and nbout 1 tun. in 
Oonsoquently to make ffull, use. of |.h.< !.j... 
of a condensation puilip, coniutciliuj 1 in' 
not less than "2 cm. in diameter miwt ln u. -- > 



22 



ATH-PUMPS 



if the evacuated vessel has to ho sealed oft' 
eventually, tlio speed iii often limited by the 
diameter of tho scaling - off constriction. H 
this constriction is to lie sealed off by a blow- 
pipe it in difficult in make it iiiora titan 3 innt, 
in -internal tlijifiiotor; but it ia possible by 
heating the tube very unifnrmly ami by 
malting tlio temperature gradient along it 
very stoop (e.g. by a small electric furnace 
surrounding it) to seal off tubes 10 mm. or 
more in diameter. 

(48). Secondly, there is an evolution of 
gas from tho apparatus being exhausted. 
Glass and metals in their ordinary condition 
give off large quantities of gas when exposed 
to u vacuum, The gas from glass is chiefly 
water and C0 3 which has boon absorbed from 
tho atmosphere and will bo rcabsorbcd if 
the glass, having once been freed from gas, 
ia exposed to tho atmosphere once more. 
Tlio gas from motals ia largely hydrogen and 
carbon monoxide, absorbed from flame gases 
during manufacture and diffusing out from 
the interior, Tho evolution ia greatly hastened 
by heat and, in motals at least, by making 
thorn tho electrode of a discharge, oven if it 
doea not cause- material heating. 

To obtain a high vacuum, it ia necessary 
to heat the glass while tlio vessel is exhausted 
. to tho highest temperature that the apparatus 
will stand without collapse ; about half an 
hour at this temperature will liberate tho gas 
from tlio surface, but there ia a continual 
evolution at this temperature which ia generally 
thought to result from an actual decomposition 
of the glass ; this evolution stops when the 
glass is cooled, but if tho cooling ia too rapid 
some of the gas may condense on tho glass 
during cooling and be evolved slowly again. 
Ifor some purposes it is desirftWo to enclose the 
apparatus in a, vacuum furnace, so that tins 
external pi'L'ssuro of tlio atmosphere is removed 
and the glass can bo healed for some time 
beyond tlio softening point without collapse. 
Tho metal parts must also bo heated to near 
tnoir molting point line severnl hours ; this 
heating is effected in modern practice, either 
by malting tho motal the target of an electron 
bombardment from on incandescent cathode, 
or by oxoiting high-frecruonoy eddy currents in 
tlio metal by coils surrounding tho apparatus, 
Much time onn bo savntl by beating tlio motals 
in a vacuum before they are introduced into 
tho apparatus. 

By long-continued treatment of this nature 
tlio evolution of gaw can be stopped and a 
vacuum obtained which la perfect so lav s 
the most dfljiuato nwinomotors can to]], and ia 
maintained indefinitely it the vessel is gas- 
tight, But if the exhausted apparatus is 
aoalocl oft from the pump, some gas is always 
introduced by this operation. If'or in order 
to so/ton (.lid glass it must bo lioatot! above tlio i 



temperature at which an inexhaustible ovolu. 
tioii of gus starts. Tho gas lima introditml 
can bo diminished by heating tho Healing-till' 
place to near its softening torn pora turn fur 
sonic time before sealing, and then co 
tho soiling &f> quidtly a-s possible, 
much of tho gas (chiefly water vapour) UIUN 
introduced disappears, boing either 
by tho glass, or " cleaned up " by a 
subsequently passed tlirough tho vessel. But 
it scorns that, whatever pneciuilifm in tfilton, 
tlio most iltjiuato forms of manometer 'ill 
always dotcet tho presence of some gas in a 
vessel immodiatoly after it ia scaled off. 

For furthor information on thcso points 
reference is inado to (83), which is tho IHIHI 
summary in English of the. state of tin neb 
which ia described in patents rather than in 
scientific journals. Some important dovint'H 
are still kept secret. 

I). MISCELLANEOUS METHODS OP 
EVACUATION 

(49). It remains to consider some other 
methods of evacuation which, though thoy do 
not satisfy any definition of a pump that. 
would liiivo Leon acceptable twenty yearo atfo, 
satisfj', ideally at least* that gimi (it Urn 
beginning of this article. Home of thorn arc, 
and still more have been, of great praulinil 
importance ; and they do not appear to dill'cr 
more radically from the older conception of a 
pump (winch implied a nioeliftiiioftl dwicn 
with moving parts) than tJio diJl'iiaion piiiii[V). 
Their chief modern UHO lies in the potifiiliHII.y 
thoy provide of evacuating a portalilo veswel 
soaled off from all fixed apparatus, 

(00) C'ounnNSA.'1'iON. Tho presaum of tlm 
gfts in ft vessel can bo reduced by <n'liitf( 
suJiTicionUy any jwirt of it wnlla, Tho limilJit^ 
pressure) obtainable by thin means in, of tmimii', 
the vapour pressure of tlio Hiibstamto at Urn 
lowest temperature available, Savory, when 
ho evacuated tho cylinder of his H(.oikin-|iump 
by condensing tho steam with ft jot of wnl,r, 
was using this prinoiplo. It has bad 
nioro modern applications, e.g, when a 
such as air has been removed by (linpl 
it with C0 a and then condensing UMI 
in 'Jiqtiid air. Tho mothod ia also uwd fur 
compression. Oltlorino, CO B and fiO t Ituva 
been comprosBcd into containers by cimilt-UMn- 
tion in placo of by compression pumpH. 

(51). OIIMMIOAL ACTIOK, Oas nun ahio In* 
removed by causing it to react (liiomii'iilly 
with tho formation of solid or liquid com- 
pounds. Gns analysis by " absorption " irillt 
liquid reagents employ's this priniiiplci, 1m t 
aomo dovolopments of it nond moro Hjie^iul 
montion. Thus it has boon shown (!M) tlni.lv 
inotallio oalouim hcatod to 700 0. will winMim 
with moat, if not all, gases, except tliomi uf 



AIR-PUMPS 



tho iimotLvo group, to form solid compounds 
with low vapour 'pressures, lint some of 
the- oompmmtlg, especially the hydride, have 
conaidorablo dissociation pressures at slightly 
higlior temperatures, and tho toinporaturo of 
tho mtal must bo carefully controlled. Tho 
method has its uses in special circumstances 
(e.g. whore high vacua have to bo maintained 
away from a laboratory or supply of liquid air). 
Tho alkali mofcals will also combine with all 
active gases ; the combination is usually 
brought abtmt by tho electric discharge. It 
has long boon known that a discharge passed 
with a cathode of sodium or potassium 
(more- conveniently the alloy of the two) will 
remove, the common gases down to tho 
pressure wlioro tho discharge ceases. Tho 
latest development m tins direction is absorp- 
tion by heated thorium or zirconium (35). 

(52) AnaoiirTiON. But such chemical 
methods hfwo been littfa practised since tho 
discovery of the powerful absorption for gas 
of charcoal at low temperatures. From the 
discovery of the method by Dowar (86) to tho 
invention of the molecular pump in 1013, 
it was tho standard method of producing 
extreme vacua unattainable by liquid piston 
pumps. A glass or, preferably, silica tube 
containing a. Tew grams of charcoal is attached 
to tho vessel to bo evacuated. Tho charcoal 
in heated (hiring tho preliminary exhaustion 
of tho vessel, which should bo carried to -001 
mm. ; tho vessel is then disconnected from tho 
pump ami tho charcoal tube cooled in liquid 
air. H the vessel is largo and the highest 
vacuum IB required, two or more charcoal 
tubes may ho attached, ono being sealed off 
before the. next is cooled. 

Many experiments have been made on (I) 
tho relative amounts of different gases which 
charcoal will absorb at different temperatures 
and (2) tho absolute amounts absorbed by 
charcoal prepared in different ways. A full 
discussion of tho results is beyond tho scope of 
this article, and for fuller information reference 
may bo made to a good summary in (37). 
As regards (I) it appears that, .in general, 
gases arc morn absorbed tho higher their boiling 
points, the exception being the inactive gases 
which are but slightly absorbed. The mass 
absorbed is proportional to tho mass of the 
charcoal ; it increases aa tho temperature is 
decreased and as tho final pressure of the 
residual gas is increased ; it is doubtful, 
therefore, whether Ji really perfect vacuum 
could bo obtained by tho method in ideal 
conditions, bub, as with tho diffusion pump, 
tho actual limit lies beyond the range of 
measurement. Tho rate of absorption de- 
creases greatly aa tho equilibrium pressure 
is attained, and, though tho speed of evacua- 
tion is rapid compared with that of any 
piston pump down to -0001 mm., it is probably 



slower than that of the Langnmir pump at 
lower pressures. 

As regards (2), there is some conflict of 
evidence which has been only partially removed 
by the very complete study of the absorption 
by charcoal which resulted from its use in 
gas masks during the late war. In general 
tho denser charcoal from the harder woods 
shows tho greater absorption ; the shell of 
the cocoanut and the kernels of some fruits 
are the best raw materials. Tho original 
coking should bo at a temperature not exceed- 
ing 900 C., and must be followed by some 
process for the removal of residual hydro- 
carbons. For this purpose heating in a stream 
of chlorine at 800 followed by heating at tho 
same temperature in hydrogen has been 
suggested ; but the best modern practice 
appears to bo alternate absorption of air or 
oxygen at atmospheric pressure and liquid 
air temperature with " out-gassing " of tho 
absorbed gas by evacuation at 400-500 0. 
Some writers maintain that all absorbed gases 
can be removed by heating to 600 C., others 
that heating to any temperature over (500 im- 
pairs the subsequent absorption. It has been 
found also that charcoal, activated by special 
processes, will produce high vacua even < 
atmospheric temperature. 

Absorption, similar to that of charcoal, 
displayed by other finely divided solids. ] 
fact, all solids probably absorb some gas at a 
temperatures, tlis differences are merely > 
degree. Of the other solids proposed fi 
practical evacuation, palladium black (whit h 
will absorb other gases as well as hydrogci .; 
and finely divided copper may lie montione I, 
In addition reference may bo made to tho m .- 
usually great absorption of hydrogen by tni . 
talmn at atmospheric pressure. Here aga n 
reference may be made to (38). 

(53) ABSORPTION IN THE ELECTRIC Di 
CHARGE. In the early study of X-rays it wi 
found that a hard tube often became " harder 
by tho passage of the discharge through it ii 
consequence of a disappearance of part of th 
residual gas. This disappearance seems to b 
a normal accompaniment of tlie discharge 
when it does not take place, or when th 
contrary process of an evolution of gas occurs 
it is because tho normal disappearance i 
obscured by an evolution of gas caused b; 
heating or possibly by some other and distinc ; 
action of the discharge. 

The' faots concerning this absorption of ga i 
are still obscure, and still more obsom'e 
explanation ol them, It is certain that 
inactive gases are in general less absorbed I 
others, but whether and to what extent 
nature of the electrodes and of the \\nna 
determine the absorption is not yet certain. 
Here reference will only bo made to those 
actions of the discharge in " clcaumg-up " 



'M: 



AtR-PUMPS 



l^an u-hieh ivrn of practical iiiipnrl-iuico. A 
ffonoral rnrnixuico may bo givon bo (H9). 

Tlio fiiml ovarimtion of nin:h appni'atiiH as 
llitirmiimio valvc-s, niuliuoi'H mid X-ray tuhes 
in pi'obulily (stTuolud by thn disohargo. How- 
ever mri'fidly tlio ttppaniUis in evacuated by 
pumping, uomo gfiH IH alwayt) intmdiiced in 
muUiiiK off from tlio pump. '1'hia gaa IB 
lai'tfoly, if nob mthuly, u.l>snrl>nd by tho walla 
ami i-hiiitriJiUm hctoro any disohurfjo passes; 
bub during tho iirt fow momenta, of bho dis- 
isharyo, wliidh ropreKimtH tho normal fwnotion 
of thfi npnuvatiiH, Kiiino Jui-Lhoi 1 clmngo occurs 
\vliioh imilus.! tho " ('.loan-up " inoro oomjiloto 
and mom pdriniiiujnt. 

Ib huti loiuj; been known tlmt tho passage 
o( bmi dinnliiirgo IjuUvRirti Hintiiblu eloctrocles 
wotihl proinobo olunniuul notions which lead 
to Uio romoval of gas. An itiHtiuico is provided 
liy tho diHohar^n Imtwimn nloctrndcs of tlio 
11 mislulrt, \vliiuh him been already mon- 
\f<;iun, it has hoon found that a 
pansiiif! to (in oldctwido of oharcoiil 
ijiuino Lin; ohitrooiil to nbsoi'li at afcmo- 
boiiipmuturo an it -\vill aliHorl) without 

til liqiud-mr tomporaburo (40). 
S {fi.|),--Uul tho most pracitieally imporb- 
iuit uroutiHH of ovaiiinilion dopondonfc on tho 
<liH(!luirj( in blmb which involves tho introilnti- 
lion of ])hoH]ihonm vapour into tlio ovacuatod 
vcHHi'l. It n.]i!'iu'rt to liavo bom diaoovorod 
lirnt liy Mitllftiituu (-11)1 it wan n]>|Uod to tho 
nvaniiittioii ('[ (ihmLrio iiKiiuuloHCGiil lumps and 
IIHH IKHIIL iiwd for the HIUHU ]Jiir]iriHB cioiitinu- 
oiinly niniio if-!* diHiiovory. At first ib appcara 
to hiivn lu'H Ihou^hb that tli action was 
olmmimU, but ib in now known bo Im dopmulent 
on the IIIHIHUKO f Jt diueluu'Ko bliroiiKh bins 



V 'Tl'ui ox iwli iiiiiiilUioiin wluch dotorralnn tlio 
rHiii.i'umiuit of Mm HH JIHI tlU (jlwouro, 
hill, il may IH.I Htnttiil Kiamnilly tlmt if a ilia- 
olmmit IH jiiuwdil UirowKli any mixture of gas 
iir viiniHiw nonlnlnln plumplionia vnponi' tlio 
iin'HHiiw will \w Hiiliinud mom m]iitlly and do n, 
Wr Umll Hum it would 1m if tho phoRpluiraa 
vaiHitu- vmvci ulwHUl. Tho ^^ H^b UIH (l! ,1- 
aimi-awil mvn 1m iimtuiwl liy howtiiiB tho walls 
,.[ Ui vofwtil tii ft tftinpnmbuio at wluoli rod 
ohoHphorim will oviviicimto. Tlio latest theory 
of tlu. iwtlcm (42) in that tho ff w is doinwitejl 
mi Lliu wnllH and cj<.v*irod with a varnish 
i>r rwil pliiwphin'HH iirmluand by tho notion 



pusses between tho oppcmibn ci** ri1 
of tlic iilinnont which net as olcdbrudon ; (*'' 
catlioclu, bDing inuatidosuoiit, gives a thcrminii^' J 
omission sumoieut to abolish tho catiiodn *"-' 
of jjotcntial and permit a discharge tn |)JL:'- 4 
uvon when tho potential differoneo Imtwi*'" 11 
tho olecitrodes does nt exceed fifty vltn. 

Tn Jltulignani's original method tho p1n : *' 
plioniH vapour was introduced by hi-fU-iiii^ tlr 
Htmill qiiiinbity of red phosphorus in tlio l-u' K " 
oonnoeting tlio lamp to the pump jimb bi<f >l ?* 
sealing off, Tho labor practice is tti d(i| til(l 
the red phosphorus 011 tho filament or Ui" 
adjacent supports, whence it is oviipornti^l tv /* 
soon as the filnmont is heated. Nowiidii,^'^ ** 
is also usual to depoait on the filament, fcugol-1 * " '** 
with phosphorus, salts such as fiuoridrH H>l " 
chlorides. Various benefits are aUi'ilmi<'< 1 ' '* 
tho preaentso of thcao salts, but it HceniH l. ' '*" 
agreed that thdh' action is subsidiary to l-l^' 1 - 1 
of tho phosphorus, and that tho evaeiui.1 " *** 
would not occur unless phosphorus (or <mo * ^ 
the other olomunts incntionod) were proM^i^l - 

By this process of phosphorus ovaouiLi*' ' l - 
the ' USD of high -vacuum pumps in Ij^rni' 
manufadtiiro ia rendered uimeccHsary. h^-* 1 i 
if the piim]) leaves residual gas at a pi'<*MHir 
of 0-1 nun. in tho lamp, almost all this KUH \vilt 
bo ronioved in tho fit-fit few seconds of " litn i 
ing," and tho prosauro reduced to ICIHH Uun* 
0-01)1 mm. No morcuiy-pumps are now in<*-l 
in lamp-making; oil-pumps, usually of < 'l<i->-* 
Ad, aro Hiifficicnfc. 

The same method has been applied to it'll*'* 1 
cominoi-dial vacuum apparatus, c,g. roislify **M 
valves of tho old typo without an miunKU-m-* 1 *!* 1 !- 
oathodo (43), and, moro rarely, to tho mmi<i n 
thormionio typo. . H. *' 

IlliFBllMSOBS 



1. Vf. fliicilo, Pints. Heit., 101!!, xlv. I2:m. 

a. S. 1'. 'I'liomiwiin, Tha JtevelaiHiifitl <>J tin' .1 
ctiriiilAir-l'inufl, 1888. 

It. Jl. W. Tnivm. The (tturlu vf (Jaws, 111(11. 

I. .M. T(il>Lor, J)inal. Print. Jmtrn., 1HIW, >'l 
\''(\ 

ft! .11, IhiKcn, iricrf. Ann., 1881, xll, -Illfi, ; 



.\f*-r 



]ii'ovonbn tho ru-o volution of tho g(is 
t n Mi" " varninh " remains j ib is 
Unit tlio. *>x! optional eleofcrionl 
o( tho NhciuplioniH vn-pour aro_ of 

(ivi ,. [.t in knmvii tiliftt milplnir, iodino, 

ariiijnto ant in Hinmwlmt tho sumo way as 

in thin inabtoi', 

In mv iiwftiwloBoent lump tho- noooaBury 



7. 
8. 

Ilrlt. 
10 
II 

13 
H 
16 
olv. 
10, 
17 
18 
II) 
20 



,, , . --. 1 

U. Stoarh ami J. Swan, li.A. Itw., 1H/*1 I' 
1'at. rOOU/8l. 

, Knaineeriitg, June 24 nnd July H, HtJI . 
. Hie WcWrtse, A. v. IhcrinK, 1UIS, 
. Xciiner, JJs famnnotiv-Jilaerohr t 180.1, 
. I\I. Volmcr, C7!. .He) 1 ., 1010, lii. Hill. 
C. .It. Iiint!, I'lte. [fan, 1018. 
A, Kmulfc and U. Warburg, Poga. Amt., 

i. Ji. KmiiiHdii. viiin. rf. Phi/a., mnn, xxyiii, 

. W. flacilu, Ana. <l. Phut., 113, x . Ufjlt. 
W. Oawlo, Ami. A. Ptos., IDI3. N 1 Hi 7 
W. (incilf!, Ann. d. Phi/s., 1015, xlvl. .ir. , . 
T. liiuiKimilr. PAw. Roe.. lOlfl, v I. K. 
. Oolirta, i!H. /. (A. J*ftiw.. l(1 " () - ' n * 
10(15. 



i 

24. W. W. Crawford, Pints. Set., 1017, x. f.r*T. 

25. ])rlt, 1'ilt. 108SOO. 1017. , ,, 

20. L. T. JoncsamlTl.A.IliissoU, /'Aw*. Jto'., ilM 
x 801 
' 27. Stomcus nnd Hnlslte, Hrlt Put. 1 57 1 1 H. I li t u 



AIR-PUMPS, EFFICIENCY OF BALANCING 



2ft 



cliUu-, I). It. I 1 . 'Mm2, I in 7. 
.rails, J. A.IH. Viieui. A'oc., l'JI7, ,xx\lx. 
SIBIL 

JiU, JU' l .Stii]isoii,./."ll'ns/i.jlffH/..S'ci., M)l7,vll..|l7. 

81. M. Volinor, Hrll. J'.-it. 140313, HIM). 

;t-Jl. Wiffltot-n .li[i>t;h'Lt! tin., Jlrit. .Put. 1387'iG, I01. 

!1JI. S. JJiinliiiiiii), (tt'iu-ml J'Hri'.trir, 2tftww, 11120, 
sxill. 078-<WU anil 1021, KNlv. a-l 8-!ifi!i. 

:M, E-\ Kmidj-, I'nx: Jloti. Woe. A, 11)07, Issvlli. 42S), 

:if>. .lirJLiiil) 'I'liomsini- JIousLon (.'o., Jlril. I'nt, 
U)!):t08, ID Jo. ; 

3fi. J. J)nwiu-, J'ruc, I)v>i. fioc. A, 101)4, Ixxlv. I S3 a. 1 

y?. S, Dii.tluiitui, Gr.nerat Kke.lric Jtcvieiv, Mini, ! 
xx Iv. C3-OCL 

:iH. H. J>nshninn, (leneral lllertric Jleeieto, 1921, 
x-\lv. 21-1-248. 

Hi). S. Dmhtniiii, (ie.ntml Klcclric Rctww, 11)21, 
xxlv. i)(S-f!8. 24ii-2.Kl. 

JO. A, J[. I'fnml, /'Ays, /ert., 1012, xlll. 871. 

41. MiiUaimnL, Itrit, J'nt. 101211/04. 

'!^, llcacaruli Stall' of tlio O.Ji.O. Ltd., London, 
/'/if/, jl/fiff., 1021, xll. G85. 

13. O. Lodfie tintl otlitM-s, Brit. 1'at. 2GO-I7A/05. 



See 



Air- 
; Air- 



Alft - 1'UMI'S, 'JSl'l'IOIENOY OF. 

imwi|M," (5). 
AiRSoiiuwa USED AS PuMi'S. Soo 

j)iinj[)s," (35). 
Aiu TilBiuiOMETJJB, Sec " ThormodynamicH," 

H). 

Ant VESSEL MKTHOD or .LHVEI. INDICATION. 
Sco " llotiVra, Liquid Level liulieutorn," 
S (Ifi), Vol. III. 

AuUMINIUM, A'L'OMH! HllAT Ol^, AT L()\V 

'rjJML'UHATUHKS : Nomat's valuoa tof, 
tiilniliitod. Sue " (iUiiriuiotry, Elccstrkjal 
AlftlhmlH uf," (11), Talilo VI. 

AI.UNJJUM. '.L'Jii) trade name fm* a tubing cum- 
]K3(jd of fused, alumina (Al a O a ) witli a, bimi- 
iug of firciiliiy ami naod as a protcoting slujnth 
ff)i - a tlitjrniooloniont at temperatures np to 
15CO" 0. .Sco " Thcrmooouplos," (i) (Hi.). 

AMAOAT i INVI^TKIATIONS ON TUB EXI-AHSION 

OF FLUIDS VNDHIl HlOU PllESSUJlEiS. SOO 

'' Thcnuii,! Expuiision," 1 (18) (Hi.). 
AMMONIA, LATENT HEAT oe VAL-OIHSATION 

OP : computed, by various writers, for 

tlHToront toinperatm'ca, and tabulated, Soo 

" J-riitont lloiit," (7), Table V. 
ASUIONIA - ABSORPTION REFRtOBWATINO 

MAOIIINKSI. So " llcfrigtratioii," (5). 



AMMONIA CoMriiussioN KKFHHIKRATOH. .Sen 

" J.tfrigrati(ii," (2), 
AN'OUHWS: INVKSTKIATIOKH ON TIL n EXPANHLUN 

01-' .KUJIDS, IN I'AKTKJIIt.AH (.'AHHON 1>]OX11)K 
IINJlETt Hl(l II PliKfiSUKJiS. See " Tliorilllll 

KxpiuiBMHi," (18) (ii.). 

ANII.IN, Si'EiJK-'KJ Hi'iAT OK, dutoi'niinod by 
I'j-of. JC. 11. Olrillitlm by tins ohnitriiuU 
nictliod. Soo " Ciiliiriiiuilry, KLuulrkui-l 

of," (fi). 

fjii IJjfAKU. Sat! " .Oyiifuuomcturs," (S) 
(ii.). 

Anon KS. Sco " Hti'iustui-L'S, Stiriigtli of ," {^7) 
AiiuniiinDEAN SCREW. Boo " JlydnuilicM," 

(33). 

AucmiiMHDiis' PiiiKOiri,]!. T3io roHiilUut. of 
tUo proamii'ca uotitig on a body humored 
in a fluid is equal bo tho weight of lluid 
diaplficod and nista upwards througli bliii 
centre of gravity of tlmt Iluid. 
ATOMIC HMAT, VARIATION ov, WITH TMIPKUA- 
TURK, Sco " Calorimctry, tlio QuiuiLiini 
Thooiy," (d-ii). 

HEGOIIDIMO APVAHATUS : ]. ( Vn' 
ILBO in StrongtU Tests o MatorialH. Hen 
" Elnaliio CoiiFttfUits, l){(t(.Tiuina('i(n of." 

Nt(!(id J. 3 nl.(Mit Wpring Buluiuicul 
llwoiniloi-. (01) (ii.). 
Ualby's Optical Hmjtirdcr. {(11) (v.). 
Goneral Mothcids tulnpUsd for Ddwign of. 

S (fiO). 

Konncdy-Ashciroft Jteeordtir. (111) (iv.) 

Itooeo's .Uooortler. (til.) (iii.). 

lliolilo Autiigi'upliic and Antnniatio A]i|Mii'ii- 

tUH. (00). 

ii'L'oMoiiELio EHOINK, TIIK VAIJXHAM., Hcn 
"ViiLrot Kngitut, Tlio Wdtor-cooldtl," (It) 
(ii.). 

vdOADRo's LAW. Al any on toinporaliirn 
and pi'OHSiiro, oiiital volinnoH of dilTtsrout 
ganoH oonfciiin tlio satiio number of iiioluonIoH. 
WhiEo (ixiiot fur " ])cffout " ^notss only, it in 
approximately Iruo of voul gascn. Hfi, 
" TliormodynuniioH," (0(1), 



B 



STEAM METER. Soo " Motors for 
jrousuromont of .Stoum," (20), Vol. III. 
BALANCING. Seo " Engines and 'Prime Jlovors, 
Balancing of." 

of Driving AVlieels of Locomotive. 



of l.i'oiu'-oylindor Engines : In- 
,oliiHinn of Vwlvu-gcui'. (10) (i.). 
of Frame- lAmsua. (2). 
of Internal Coiulmation Tilnginos. 



(4). 



of Loootnotivos. 
Jialaiioing in Practical Case. 



JinJajiomg for I'rimary and frloi^imdary Forni'h 

and (JonploH. (10). 

Balancing of .KiMiipniiMilmg JMuHsoo. (1Q). 
IJftliuieing of a, Itutor, (K). 
lifUtmcing (f Yarrow KohUolt Tmiddy 

Engino. g (11). 
Contrifiigul Conplo, (.1). 

Couple OIOHIII'O. (ft). 

Dtilby'a Motluxl. (C). 

DoiUietions from ]?or<jo and C'onplti Polygons. 

(?) 

.Forco Olosiiro. {(!). 
Four Masses on Four Arinn along 11 Sluifl-, 

(7) (6) and (c). 



20 



BALL-BEARINGSBOMB CALORIMETERS 



Motion of Connecting Hod. (2) (hi.). 
Motion of Mii.su in a Circle at Uniform 



. H2)(10- 

Motion of Mass in a Straight Lino at Varying 
Speed Bennett's Construction. (2) (ii.). 

Primary Balancing. (10) (i.). 

gaiter's Method of treating this 'Problem. (8). 

Seen mlary Haluncing. (10) (ii.). 

Special (JoiiHU'iietLon for balancing of Pour 
Mfl-sssos. (0). 

cimplo closure 

Tho o ^uatinn M= ma s {>) 



force closure 
The equation. M = - "^,-2 ..... (") 

Throo Ci-tttilw nt 120 cnnnofc bo designed HO 
that Masses inuliially balance. (7) () 
iNas : STOI-S IN THE EVOLUTION 
OP THE MODKRN BALL - BEARING. See 
11 l.'Yiation," (S8). 

AHNKH' TAIILB OP SPECIFIC HEATS OF WATER 
AT VARIOUS TiwtrioitATUHES. Sco " Moehan- 
iniil Jiltiiiivttluiil. of Hout," (1). 

ANI> HTH AGOUTI'S DETERMINATION 
SFEUIFK) HKAT OF WAT-JIB, AT VAUIOUS 
Timi'is. Soo " Mechanical Equiva- 
lent of Moat," (7). 

BAiuifi, 1880, compared gas-thermometers 
with aoeourttiry Btnndards of toinyorature 
in Hit) range 000 to 1000 ami rcoognisod 
tho iinjioi'taiUiO oE a uniform temperature 
(liHlributioii ahout tho gna - thonn'omotor 
bulb for pm*jKKJS of high - tompcraturo 
inon-HnircmonL IIo iiifcroclucod tlic tliormo- 
olomont in tho rrtlo of intormocliary lictwccn 
tho ga-s-thormoiiiotor bulb and tho tempera- 
ture to bo measured. Son " Tomporatiiro, 
llonlifiaUoii of Absolute Scale of," (39) 
(viii.). 

BJJAMS, .BiiNiimo ov: MAOAUF.AY'S METHOD 
roil HMVJSUAr. LOADS. Soo " Struoturos, 
Strength of," (10). 

UKAMH : VIOLATION UISTWBBM LOAD, SHMAII, 

BUNIUNO JIOMBNT, SLOl'M, AND DEFWiC- 

TIOH. Sea " Struoturos, Strength of," (12). 

BKAU nr, HOOHASI OYOLK. Soo "Engines, 

Tliorniodyiminios o Internal Combustion," 

(34) and (fil). 

UBAUFOY'S EXPEBIMBHTS. Soo " Ship Rosiat- 

ftiwo ami Propulsion," (3), 
BKOQVEUi'Hj, 1803, ooinparedgaa-thormiunotors 
with Booondury etandards of temperature 
In the range G00 to 1(100.- Sco " Tomjioi-o- 
buro, Eoalisation of Absolute Scale of," 
(30) <iv.). 

t-r, - COIJiMAN REKIiroiSRATINO MAC1IIINH. 

Used for cold stores and tho holds of ships. 
Ah 1 is tho working substance used. Sco 
" RofrlffowiUoii," (4). 

UffiMD TKST3 ! 

Altocnafcing Bond Tost bayond tho Yiohl- 
Potnt, Sco " Elftstio Constanta, Deter- 
mination .of," (78). 



Description of the various kinds of Bend 

Tests fur. Metals. See Hrid. (Sit), 
li'orms of Specimen and Methods of Testing. 

See ibid. (31). 
BENDING OF. MEMBERS oir A STRUCTURE. Boo 

" Structures, Strength of," (fl). 
UENKENE, LATENT HEAT OF KVAI>OKATION OF, 
determined by Griffitlis and Marshall. See 
" Latent Heat," (10). 

BERNOULLI'S THEOREM. Along any stream 
lino in a liquid subject only to gravity 
= constant, 



p being tho pressure at a jioint at a depth 
z below tho plane of reference, / tho density, 
and v the velocity. 

BJEMKOM'S CALCULATIONS FROM VOLUMETRIC 
HBAT FutuitEa. See " Gases, Specific llent 
of, at Higli Temperatures," (fi). 

BLACK BODY, invented by Wien and Lniiniier 
for tho investigation of tho laws of radiation 
from a uniformly heated enclosure) : descrip- 
tion of modern' form of. See "Radiation, 
Determination of tho Constanta, etc." I. (2) 
(i.), Vol. IV. 

BLAD-H-WIDTH RATIO von 
is tho fraction 



Maximum width of blade along its 

Radius of propeller 
Reo " Sliip Rcsistaneo and PropuMon," 

('H). 
BLADINO IN STEAM - TUIUIINES, 1^ ORM AND 

Eii-FioiENOY OF. Hco "Turl>ino, Develop- 

ment of the Steam," (3); " Stonm- 

turbine, Physics of," (Ii). 
BLOWERS, THEORY OF. Seo "Air-pumps," 

(!) 

BOMB CALOlUMKTli; I iS 

(1) INTRODUCTION. The laboratory moth'od 
o{ determining tho calorifio value of a fuel in 
to burn a known weight of a carefully dried 
sample in a vessel containing oxygon. From 
tho temperature rise of tho water in tho oalori- 
motor tho heating value of the fuel is com- 
puted, taking into account certain correelionn 
winch are described later. AKlunigh tho 
calorific value does not givo all tho informa- 
tion desired concerning a particular fuel, or 
determine its suitability for a specified purpose, 
yet it is generally accepted that tho heating 
vahio is tho most important property to bo 
considered in estimating tho value of fuel. 
Purchasers of largo quantities of coal now 
adopt tho heat-unit basis of evaluation, and 
tho technique of combustion oalorimotry 1ms 
boon so well developed that a skilled operator 
can average thirty : fivo determinations per day. 
Two types of apparatus are employed for 
auoli tests. In one tho fuel sample is burned 
under normal atmospheric pressure in a calori- 
meter of tho " submerged boll " typo, 1 whilst 

* Soo "Conl Calorimeter." 



BOMB CALORIMETERS 



27 



in tho o tlior the fuel is burned under high 
pressure in a "bomb" typo of calorimeter. 
Sonic authorities prefer tho " boll " typo to 
tho " bnmb " because in it tho combustion is 
carried out in oxygon at nearly atmospheric 
pressure and, consequently, llio conditions 
resemble those obtained in steam boiler 
practice. With a "bomb" calorimeter tho 
combustion is nlmost instantaneous and 
resembles an explosion in its violence and 
rapidity. 

Tho decomposition products of coal vary 
somewhat, and ifc is generally fonnd that tho 
results obtained with tho bomb calorimeter 
are slightly higher than those with the " bell." 
For scientific work, however, tho bomb type 
in universally used, since under good work- 
ing conditions tho combustion obtained is 
practically complete. In skilled hands either 
jrpotliod gives reliable and 
concordant results fur solid 
fuels, but the " bomb " is 
the only method applicable 
to liquid fuels, 

(2) DESCRIPTION OF A 
BOMB CALORIMETER OUT- 
FIT. The ofilorimetrio out- 
I K '"'' C01ia ' 8ts f the following 

I H elements : 

(i.) Tho bomb. 

(ii.) The calorimeter 
vessel, stirror, and 
constant tempera- 
ture jacket. 

(iii.) The temperature 
measuring instrument. 

(i.) The Bomb. In ono 
of tho oldest forms of 
apparatus tho Mahler- 
Donkin. the bomb consists of a .. massive 
gun-metal cylinder provided with a cover held 
clown by three studs. Tho cover is pro- 
vided with a milled -head screw valve for 
regulating tho Inlet of oxygen to the cavity 
inside tho bomb. The joint between the 
bomb proper and its cover is effected by 
moans of a lead washer Inserted in a circular 
groove. The inside of tho cover has a pro- 
jecting ring which registers with this groove 
ivheii it is serowe<l down. Tho bomb is 
plutort inside with gold in order to withstand 
tho corrosive action of tho nitric and sulphuric 
acids produced l>y the combustion of tho 
fuel. Tho most satisfactory form of lining 
is that (if platinum, but nowadays it is not 
much lined on tho score o[ expense. Porcelain 
enamel is ftlao somotjmes used for lining tho 
bomb. ft ^ 

Tho Krookcr .ftypo of bomb has a cover 
screwed on ta^ho bomb (see Fig. 1). Tho 
bomb is nuuto of atcol and lias a fixed platinum 
lining, while the cover is of bronze. 





Parr 1 has recently designed a bomb of an 
aeid - proof base - metal alloy which appears 
very promising. 

Some investigators employ a replaceable 
lining, but in practice it is found difficult 
to maintain a 
perfect fit and, 
consequently, 
difficulties arise 
owing to leak- 
ago of the pro- 
ducts of com- 
bustion into 
tlie space be- 
hind the lining 
where it cor- 
rodes the metal 
of the body of 
the bomb. 

Tho staff 2 
of tho U.S. 
Bureau of 
Mines have de- 
veloped a form 
of bomb (see 
Pigs, 2 and 3) in which the lid is held in position 
by a novel form of sealing device. This con- 
sists of a tough steel receiving nut and kick 
so constructed that less than a one-eighth turn 
with the wrench suffices for sealing. A circular 
gasket of electrician's solder effects tho seal. 
This kicking device is 
an adaptation of the 
principle used in tho 
breech locks of artillery. 
They claim for this de- 
sign durability, ample 
strength, and facility 
of manipulation. 
Further, when the lock 
wears out a now ono 
can bo substituted 
without tho expense of 
making and gold-plating 
a now shell. Tfie shell 
of the bomb is made of 
Monol. metal which is 
well adapted to gold 
plating. 

Fury has devised a 
bomb calorimeter in 
which tho heat devel- 
oped is shown on an indicator. See article 
on " Oalorimetry, Method of Mixtures," 
(13) {ii.), "Metallic Block Calorimeters." 

(ii.) The Calorimeter, Slirrer, and Constant 

' "An Acld-roslatlne Alloy to replace Platinum 
In tho Construction of a Bomb Calorimeter," Journ. 
Am. Chem, Son., Mov. 1016, xxxvil. 281B-2G22. A 
test of the nbovo by E. H. Jesse, Jr., Eighth Int. Cony, 
Appl. Chem., 1012, i. 233, 380. , , , L T 

3 "A Convenient Multiple) - unit Calorimeter In- 
stallatlon," by J. D. Davis and E. L. Wallace, Jimwm 
of Mines Techniral Paper, 01, 48 pp., Washington, 
1018, Abstract in Engineering, Jan. lOj 191*). 




l-'ia. ;(. 



1*8 



BOMB CALOKTMETTCRS 



'('t',t/if<.mtitrr. Jtir.knt. Tn Mm outfits employed 
in lliisi c!iumlry (ho (snlorhnotor, stirror, and 
jiinkiili i.u'o similar to those employed in 
it-ppiimtiis for Mi'dinnry ealorimntrio oxpori- 
monlH l.y tlio Motlmd of Mixtures (seo 
(!})- 

Ab HID U.8. Hiiremt nf Minos 1 a form 
of iippiiriitiifi hit a ItKon developed which is 
rH|in<iia.lly mlrtplcwl for combustion oitlorimctry 
(nen A';';/, .(.), 

Tho (snloriinnfor ia nmtlo of heavy shoot 
brass romforoed at tho top and middle by 




DnliillM ill' (!;iliirliiii)(iin': A, vortluil section; It.horl- 
y.onlnl NiinMim tlirniiHlia'birihnwlng tulmliir allrrcrwfill ; 

(J, Hllllllj I'lllhili; I), hdl'l/.OIltlll SOOllon through til' 

ulniwJnii lltl 



liniss ImtulH (not) A). A tubular stirrer well 
in MMilmwd In tko oiiloriinotur ns Hhuwii in Ji. 
An oloiitvotla in fanUmod to tho btittom <f tlio 
(itiliiriinoloi't but iiiHulatod from it, which 
nudavi (loiiiitot wiLSi llio bomb plug whan this 
in phunul in puHiliini. 

'L'lio imlin'iitiotor in supported in its jndcot 
on Lliroo ivory Htuds. TJio jaoltot IH a cylin- 
driiiiil voaaol provided witli a ortvor (if brass 
ground to a \vator -iij^ht lit. Tliis onvor ifl 
|)rnvidisd with a thin slioot-braHH wntor soul 
(ami /'((/. 4} t\\il tn llio oiwor proper liy moans 
of tJinif! Uiiti inHHlutting widn nf ivnry in snuh 
a mnumir Unit whon tho citlonmotor is in plnoo 
anil tlid (itjvcr broup;!it down snugly tlio water 
HOiil 11 in iiiiutuot wii'h tho surfuco of tlio valor 
in tho oalorinuitor, UHIH surviiig us an oiToetual 
1 Davis mill Wallace, toe. eft. 



ovapnration in(.n tho spurn lid \M' 4 ' * ' 
tho cnlorimelor mid its jaoltet. 

Soldorod to tho jiKskot nre two heavy tiivi 1 "" 
III^H, by which it ia hold to tlio vorti<ial lir* " ' 
T-bai 1 iif tho framo in smsh IL iimnnor \\n |i> \if* ' 
mit tho J!i<;l!t ID slide vortioally. Tho jin-1-.*"'' 
in Hiipportdd by a heavy helioal brnsa n|nl f *'^ 
boai'itiR affiiinHt tho bi)ttrnn of tho lanli, :''*' 
of Hiicti strength that tho jaolvet vhon ulini'f 1 ,*"" 
is hold voi'tidal viih itH top slightly ubovo * I*'* 
fliirfnco of tho tank ivator iijvainst mi mljnH* " 
nblo stop lixorl to tlio T-bar. 

Tho stirror shaft arrangomont ia alno nlmT*v** 
in Fig. 4. Tho upper part of tho nluif|. *** 
which tho driving wheel ia inoimlod omi-ii^i * '* 
of a thioU-wnlIod brass tube, into which fl* 1 * 
lower inirt of tlio shaft tolnRoopos, tho laH*'*' 
bning jirovidod with a conical piece ((') nc;nu l "' ' 
to tho end which engager n rocoivn 1 al ll* 1 ' 
lower end of tho shaft tnbo tiFlor Iho maun*' 1 ' 
of a ciinifMil fritstion clutoli whon the wlM*'* 11 
calorimeter SH lowered into place. Tho lun *'* 
bearing of tho atirror shaft in (Mirricd by (I**" 
lid bniokofc (0), which is held to (ho vcrli-' 11 ' 
T-bar of tho frame by a clamp which poruiH -' 
of raising and lowering tho lid and c|iini|iinM 
in any donirod iiosilion. 

Tho calorimeter cover has tubular oiitli*! *' 1 
(not shown in Fit/, 4) for tho thcrmomrl "''. 
Iho stiiTor shaft, and eloistrioal loads, (to (!=.* 
Ihe jacket and iln cover may bo (nl ully 
immorBcd in the tank wator during an C\JPC* * " 
inont. 

Tn tho equipment of tho Uurenu ni.v MM* 1 ** 
outfits arc mounted in one thennoHtntii'iili.y 
controlled constant tcmpnraLuro bath, 

(iii.) The '1'e.mpm-alitre Measurinff hitih-*z 
went, With tho majority of bomb oalorimd *- 
ontu'la mercury thonno meters arc fimplnv*-*! 
for Iho nioasnromont of tlio toinpnruliiro ii' >' 
of tho water. Such instruments have I !*- 
iidvantiigcs of siniplicily, ehoannisHH, 
nmddiuto aofsuriicy. Thoy have tint 
advantaged of considerable lag and Im-lt 
flonsibility nitjiiirod for work of tho liigl 
prouiHion, Tlio moronry tliormoiiuilor, iu 
over, powHCHHos tho Gorioiift drawback thut 
morcni'y often sticks in tho boro, jmrtlciil 
with a falling moniscua. This tronbln 
bo aomowliat allovmtwl by tapping the nl 
and Homo obwervorH utilise ii miniature c'Jo< 
biiKKcr for this purpose, 

Tho thermometer should preferably !M 
solid stem typo with its scale divided .to -n:!' 1 *. 
and tho sealo divisions should extond iltm 
tu tin; bulb to avoid uncertainty as In t| 
magnitude of tho emergent column, 

For work of tho highest precision a ratit 
inotrio rosistanco thormomotor in H-J I 
CHHcntial, and a description of suitahl" i 
Htrumonts for fcho jmrpoac wilf ho fmiti'l 
tho article on " Kosiatanoo 
(0 <!)) 



IB i * 
I i ! 



BOMB CALORIMETERS 



20 



('*) IVEiiTiions OF ooNmroriNu A TICST. 
(1.) (iidihmtion of the Apparatus. It is ncces- 
niu'y to clotuniiino tlio hont capacity of the 
hDiiil) and its fittings by experiment, since it 
is rarely possible to oalciilato this constant 
from the sjieciifio heat of tho materials cm- 
])liiyotl in its construction, There nro two 
stiuulnrd methods oE effecting this oalibration : 
(a) liy an electrical method baaed on tlio 
input into the calori metric system of a- known 
amount of boat measured as electrical energy. 
(/;) ]iy burning substances of known heating 
value. 

() Tho electrical method is capable of 
considerable, accuracy, sinco electrical energy 
can bo measured with high preoiMion. In 
practice, however, tho method suiVors under 
tho disadvantage that it involves elaborate 
equipment and is ti mo-consuming. Further, 
it is by no means easy to reproduce with it the 
Hatno conditions as prevail during a combus- 
tion test. Tlio electrical mothod is generally 
adopted in standardising laboratories, but 
for the purpose of a works laboratory tho 
second method is to bo preferred. 

(6) To en. libra to a calorimeter by means of 
standard siilwtanccs, such us naphthalene or 
hcMKoio acid, it is advisable to make about 
half-a-dozen combustions, sullicient amounts 
of tho standard being used to produce about 
tho average- toinpomturn riso obtained in testa 
with coal. Tins method, besides boing simple 
and easy ol application, tends to niinimiso 
errors such as thoso duo to thormoniolcr 
calibration, cooling correction, heat input 
from stirring, ote. Dickinson ' has recently 
mlotennmcd tlio heat combustions of tho 
following sulifitiinoea; naphthalene, benwrio 
acid, and sucrose or cano sugar, with a 
view to thoir adoption aa standards in 
calibration work. His results are summarised 
in Table I. together with those of previous 
observers. 

It appears from a comparison of tho values 
given by different observers for tho same snb- 
Ktaiuio that bonzoio acid is the moat suitable- 
in view of tlio close agreement of tho results 
obtained. 

.Dickinson (omul naphthalene to l>o a convenient 
material to work with, lint onro was iieci'sanry in 
bundling Hitioo a gram briquette would lose about 
1 milligram in weight pur hour by sublimation. 
iSuoroso did not BOOTH HO wotl aiUiptud tin botixoio 
iioicl for Htiuulardisaiioii purposes. It Iwa a 
smaller heat of combustion and frequently fnila to 



Dioldnsim migyeals Unit tho higher rcsulls given 
Ity ntlior observers fur mieroso may bo duo to tlio fuot 
Unit thoy may not have- corrected for tlio heat 
generated in the firing wire before the snni|)Io igniloH, 
With BiicroFto n. greator length of fnso wire hns to bo 



*[. 2G3, 



used than with other maleriala on account of ilfi 
lower inthini inability. 

Iron wii'o i frcquonlly employed Iincanso it bnriis 
instead of only melting, nnd is therefore morn certain 
to ignite din sample. Tho heat of foumation of 
iron osido is about 1COO oalorii-'B per gnim of ir* n. 
Tlio HiicroHL- specimens required about It cm. of w ro 
wnigliing ],'!3 ing. per metro, Ileiwin tho corrccli m 
for the In-lit, liberated in ita eomlmstion amoiml 'it 
tn about 2 calorics per centime-Ire. Nuphl.hah' HI 
ignited readily with 1 em. of wire. 

Ho aldo corrected for tho small iimonnt of nitrio 
acid formed from tho nitrogen eontninedin tlio osygcu. 
The amount i nciirly proportional to t!io lient 
liberated in tho combustion and to tho porcrntiifto 
of nitrogen present, and was determined by tilralion 
after caoh combustion. The heal of fwritmlion if 
IIN0 3 from N+O+'H.O IH about 231) cilleries per 

TAIIJ.B I 



Autliorlty. 


L- 

j> a 
Y\ 


<J -rtj 

' 


j 


^ 

R 


fj toh m ami, Rod air., 
lIortKborg 


\ 
1 " 


0315 




1887 


Hertholot, Vicillo . 






3002 


1887 


liorthelot, Limginin 




(1322 




18!iH 


Ilerthelol, Eocouni 




03'1 5 




18HH 


Stohnmnn, ICIebcr, 
Langbi'in 


f!)028 
(1)019 


C322 




J8HD 


StobmaiiH, Langbein 


. 


. , 


3(ir 


IH03 


Atwalcr and Knell . 






80/30 


11)0:1 


iriflolior and Wrcdo 


!)(U1 




, . 


1001 


Fries .... 


f 


0334 
03 IS 





1007 
1010 


Pisoher and Wrwli 1 




03i5 


mra 


1000 


Wrede , 


fit! S3 


0323 


31)fi2 


1910 


KoLli .... 


0(113 


t f 


, , 


1910 










1910 


.Dickinson . . 


0012 


(1323 


3i)ia 


J'1010 
\1013 



Tlio tliitu In tlio nbovo faiblo nro oxprefaeil In terms 
of tlio ID" calorie. 

gram of noid. AH the oxygen employed oniitninctt 
from 0'3 to O'D per cent of nitrogen, tlio oofrcotuni 
to bo applied for tho beabof formation of HNO a wna 
usually about 1 part in 1000. 



(4) PREl'AKATION Off THE TllST 

(i.) Solid Fuels, It is necosHary to oonvort 
tho coat into a small Imquotto or tablnicl fen- 
tho purjioscs of test. If tlio attempt in iniuio 
to employ tho aamplo in powdoi 1 form tho forco 
of tho explosion usually blo\vH ecimo tif it 
against tho interim 1 walla of tho bomb find it 
escapes combustion. 

Bituminous fuels us a rule-will form briquolten 
by pressure alono. In on-scs ivhoro iiiauiiiciont 
tarry matter is present in tlie natiirnl fitol, 
just sufficient of a 1 per cent solution of gum 
iiriibio may bo used to make tho pai'ticloa of: 
fuel adhesive, For half a gram of fuel, thrco 
drops of such solution arc enough. Tho 

1 Tiic Times Jlngiiteering iS'iyrfw(. i f ?b< aa. 1917. 



30 



BOMB CALORIMETERS 



briquettes must bo heated in an air bath to 
110 C. for at least four hours to expel tho 
last traces of moisture thus introduced before 
testing in tho calorimeter. 

(ii.) Liquid Fiteh.ln weighing and trans- 
ferring tho liquid fuel to tlio bomb, carriers 
consisting of small cylindrical blocks of pure 
cellulose are used, one of these blocks being 
able to absorb several times its own weight 
of any ordinary fuel oil. The saturated block-, 
after being weighed, is burned under the 
conditions and with all the precautions neces- 
sary for solid fuel, tho only difference being 
that a rather higher pressure is lined, in order 
to obtain a greater supply of oxygen gas in 
tho bomb. A blank teat with the cellulose 
alone gives the necessary data for tho calcula- 
tions. As liquid fuels contain only traces of 
acid -form ing elements no trouble arises from 
corrosion, -and a bomb provided with a gold 
lining will last for somo hundreds of tests. 

As regards tho special precautions necessary 
to obtain correct results when testing liquid 
fuels, it must bo pointed out that tho absorbent 
cellulose blocks sold for this purpose absorb 
moisture as well as oil, and that it is necessary 
to dry thorn before use for ono or two hours 
in tlio air-bath at 100 0. When saturated 
with heavy oils of high boiling-point they are 
also somewhat difficult to ignite, and it is 
advisable to place a little of tlio dry un- 
saturatcd cellulose- in a loose condition around 
tho platinum ignition wire in order to avoid 
failure of the test from this cause. As tho 
cellulose blocks are largo in proportion to their 
weight and absorbent capacity, a larger 
platinum dish will bo required than for the 
tests with solid fuel, and tho platinum ignition 
wire should bo arranged to hold down tho 
cellulose block lest tho explosive violence- of 
the combustion blows it out of tho dish. 

(5) QUANTITY air OXYGEN iiEQuiniii). 
Tlio quantity of oxygon required is about 
tlireo times that which will unite with the 
oliavgo to givo complete combustion. Dickin- 
son found that, when the amount of oxygon 
was much less than two and a half times that 
required to unite with tho combustible charge, 
there were often cases of incomplete combustion 
as indicated by a reduction in tho total heat 
liberated, as won as by the occasional presence 
of a slight amount of soot and by tho odour 
1 of the products of combustion. 

Since tho usual pressure employed in routine 
tests is 20 to 27 atmospheres, or 300 Ib. to 
400 Ib., it is advisable to have a small back- 
pressure valve inserted in tho milled -bead 
screw in the bomb cover in order to avoid 
a groat loss of gas when disconnecting the 
oxygon supply pipe and gauge from tho bomb, 
after filling tho latter with oxygon. At those 
high pressures tho combustion of tho coal 
is praotically ; instantaneous, and tho thin 



platinum wire usod for ignition 
generally be found fused owing to the toin |i 
tiiro momentarily attained. In order l<> 
teot tho platinum cnpsiilo 01- crucible from 
same effect, and from tho action of the nui 
slag produced, it in necessary to lino H "" 
thin asbestos board, cift and shaped to fit 
cnicililo or capsule. This asbestos board i' 
bo dried and ignited before USD in ordo: 
remove all matter that might vithtto 
results. 

(G) CALOKIMKTBY m r COMBUSTION v 
SODIUM PEKOXITIR. Fusion with wnd 
peroxide is tho only way known for liii' 
the heat of oxidation of elements 
not burn in oxygon and which form 
insoluble in acids, Tho method i 
to tho determination of tho bout formn 
of tho oxides of a metal and also tlio 
combination of metallic oxides, with Hi)*] 
oxido. 

Tho method is indirect ami tho heat o 
sought is not tho observed offeiit ; 
burning in Compressed oxygon is 
where possible. For examplo, whim oiu 
is burned with sodium peroxide tho oliHi'i 
heat (a;) is tho result of tlio following roiuit 

2Na a O a + = Nii B CO s + Na 3 0, 

and * equals the heat of formation of ciiu 
dioxide plus tho bout of combination of <mi 
dioxide with sodium oxide, and lows Mm 
required to separate two atoms of ox; 
from two molecules of sodium poroxido j I 

IB = + 20 -h (Na a O + C0 a ) - (2Na,0 !- SO 
BO that 



Moreover, many substances do not givo ' 
sodium peroxido sufficient heat to fno 
mixture), and honoo some readily comlitiH 
substance, sueli as sulphur or carbon, J 
bo added which gives in many cases tho \f 
part of tho totnl beat effect, I'rnfranor Mia 
of Yalo University, who has made an oxlc*i 
study of this method, gives tho following m 
obtained, by fusion with sodium poroxid( 
comparison with those- by combimUoi 
oxygon. They are : 



lUxiiiUuii. 


^ 

Z "a 
i 5 
oiR 


" H 

a a ^ 

a a? 

Ill 

u- 
(14-7 

3184 


]lClll'IH5P. , 


o-i-ao^c'Oa , 

TI+a(>=T10j . 


m-i 

216.0 


Amer, Jaunt. Knit 
xxix.lBO; ill mi 
484 
Ibid, xxvil. n-lfl 


BFo-HOFo;tO,l 


307'C 


305-2 


Ibid, xxxvl, &> 


Both values for C+20 are for noot; 
carbon. Ono roaaon for tho highoi- i 


1 American Journal of Science, 1017, xllll. 2,' 



BOURDON GAUGES BOYLE'S LAW 



31 



found in the sodium peroxide niotliocl i tlmfc 
the carbon and peroxide wore mixed in d 
mortar, thus allowing tho peroxide to absorb 
a little moisture which added to tbo heat of 
the fusion. Tho value 2(i7-5 for ,'H I \> + 40 ia 
derived from the results of fusions of iron, 
ferrous oxide, fordo oxide, and the mineral 
magnetite with sodium peroxide, and 205-2 
was the result of burning iron in oxygen. 

Sodium peroxide absorbs water rapidly from 
the air, consequently it should bo exposed 
as littlo aa possible, as the hydrated peroxide 
will give more heat with a combustible than 
the anhydrous. One of two samples, that 
which gives off tho less oxygen when fused, is 
the bettor one. The error from tho water 
content is small in good peroxide. Its effect is 
further diminished when carbon, for example, 
is added to make a mixture fuse, because in 
practice tho hoat effect of tho carbon is 
found for the carbon and peroxide actually 
usod. 

Various substances may bo added to a per- 
oxide mixture to increase tho temperature of 
tho fusion. Mix tor has usod acetylene carbon, 
sulphur, and lamp-blaok. Pure rhombohedral 
sulphur in fine powder would appear to be tho 
best of the threw, but it becomes electrified 
when shaken in tho bomb with tho other 
ingredients and sometimes sticks to the bomb 
and is not completely oxidised. Sulphide 
is formed, and oeea-sionally free sulphur is 
left. When tho bomb is much blackened by a 
fusion with sulphur tho heat result is low. 
Acetylene carbon is tho ideal substance to use, 
but difficult to obtain, 

One part of tho carbon requires 13 parts of 
pure sodium peroxide for combustion, and it 
is best to take about 20 parts in determining 
the heat effect of the carbon or lamp-blaok. 
For tho combustion of sulphur double the 
calculated amount of poroxido should bo used. 
Oxygon is often evolved in a combustion from 
tho action of an acidic oxido on tho sodium 
peroxide, and the heat required to sot it free 
from tho poroxido IH added to tho observed 
hoat. This correction, 1-73 g.-cal. for 1 o.c. 
of oxygen at Q and 700 mm., is derived from 
IJekotoff's Na a +0 = 100'2G Cal. and do For- 
crand's Na a + 20=110-8 Cal. 

Apjmratita employed for t7ie Tcsl-s, Tho 
bomb is made of sterling silver whilst tho top 
and fittings are of brass. 

Tho mixture under lost is contained in a 
cup of fine silver supported in tho bomb by 
its upper edge. A fusion in the oup cools 
more slowly than when in contact with tho 
cold bomb, and hence tho reaction is more 
complete. 

Tho general arrangement of tho apparatus 
is identical with that employed in fuel calori- 
metry with the addition of bulbs for collecting 
any oxygen sot free by fusion. E Q. 



HUPPLKMKNTAHY 

" tiur lea i:lmloura do combustion et do formation 
dcs ciirbtirc3 d'hydrogtoio Bolides, ct clmleur de 
combustion et do formation des snores, hydrates do 
rarbono ct aleoola polyntomiques congcnt'rcs," 
Bortlielot ofc Vlelllo, Ann. CImn. 1'liys. (li), 1887, x. 
lip. 483 anil 45G, 

" Uber die Methods dor Vcrbrenmuig orfainlBClior 
Subsliui/en In Hauorstoll' liol liohnn Drurku," 
SLiilnniHui, Klnber und Liinsboin, J. 1'rnkl, C'lmn,, 
.1881), xxxlx. 5011. 

" tJbor don Wilrnio worth von CnrboiiBfiiiron dcr 
ni'omatisehcn Hciho," Stohmunn, Klcbor und 
Lsingboln, J. Prukl. Cficm., 1880, xl, 128. 

" Oiler den Wtirme worth dcr Oxnlsaurerellio," 
Stohniann, KLobcr mid Langbetu. J. I'rakl. G/ietn,, 
1881), xl. l!02. 

" liber den Wiirmowcrth dcs Mcthylalliohola und 
fester Mcthylilter," tftohiiiaini, Klebur und Lanqbcln, 
J, Prakl, Chcrn., 1880, xl. 341. 

" ttber den Wflrmcworth von Kohlen hydra ton, 
mehrsiiurlKoii Alltoholcn und I.'lienolen," Slolmiiuiii, 
J. J'f<t/;t. Chan,, 1H!>2, xlv. 30ii. 

" Vbor den Wiirmoworth Isomcrcr Siiurcn von dcr 
Sinsuin monso tziHiH C,1T 0, mid C! B II a Oj," Htolmmmi 
und Liuigboln, J, Pmkt, Cltem., 1801, 1. 388. 

" Chalcurs do combustion," Bcrthclot ot Lngluln, 
Ann. Ghlm. Phys. (0), 1888, xlll. 321. 

" Hur In niosnro dcs chaloiiM do combustion, ot 
chaloiirs do combustion do divers composite organl- 
(inea," Jiertliclut ot Heoonrn, Ann. Chim. Phys. (0), 
1888. xlil. aa, if()-l. 

" iJcacripUoii nf a Boinb-Cnlorlmctor and Method 
of its Use," Alwator and Bncll, J. Am, Client. .S'oc., 
IDua. xxv. Oiii). 

" (!bcr die Vorbreiiiiimgswurmo elnlgcr orgnnlscher 
VcrbiiiduiiBOii," Fladior und F. \S r redo, Silzltcr. <l. 
Jicrl. Ai-iid., 1001, xx. 087. 

" C'oiiocriilnH Urn Adlnbatic Dolermlnatlon of tho 
Heats ot Comlmstlon of Orimnlo Hubatnnecfl, espoci- 
nlly Sugar und BoiiKol," Mlclinrds. llomleraon and 
1'YiiViirt, Am. Acaii. Prof., lOOfi, sin. 673. 

" Unto (if Combust Ion and Pressure developed in 
a Calorlmolric Ifumb," .licnodlct and I'lctclier, J. Am. 
Cfiim. Son., 1007, xxlx. 7UO. 

" Obcr dlo BcHtlmnmiiK dor VerbrommiiKHwHrmo 
orBfinlsclusr Verblndunfiuii mil iUiiiutxmiR des 
Pliitiiiwldorstfliidthevinomcters," I'lHtlutr und Wredo, 
Us. I'luis. C'ltem., l!)0!l, Ixlx. 218. 

" J'jielmng dca Variircimungskalorlmctcra unit 
Arbeltwolae," .llnUi. Lieb. Am., 1111(1, iscchxHl. 210. 

" Sur In chalfitir iln conibiiHtion ilo quclquea (Mrlvds 
]iydronanlitl)ii]6i Unies," Loroux, CM., 101.0, ell, 38-1. 

"An Adiabatlo Calorimeter Cor tlan with tho 
Cftlnrlmctrlo Eomb," lienedlct and Illgghm. J. Am. 
C'hcm. Hoc., 1010, xxxll. -101. 

" (Jbor dlo Ticatiimmniff von Verbronnn lifts wit rm on 
ml t tola dcr kalorimetrlsclion Bombo untor JicnutKimg 
dca I'latinwldorHtandthermomoters," Wrodo, Zeit, 
1'hl/s, Olicm., 1010, Ixxv. 81. 

" Jixporlmonta on a Bomb Calorimeter," AHnut, 
Engineering, 1010. xc, 755. 

" Tniluenra of Variation in ftiiecluc Hoat of Water 
on Ofilorlinclry of Ifiiela." Loeb, ./. Ind. ling. Cliem,, 

1011, 111. 175. 

" A Now Method of iKnillon for Bomb Cnlori- 
mntcrs." Iloolirlnh, 1'Hglith Int. Cong, Appl. Cham,, 

1012, x. 200. 

BOURDON GAUGES, CALIBRATION, ADJUSTMENT, 

AND COBIUiOTION FOR TffiMMRATURH OF. 

SCD " Prcssuro, Moasuromont of," g (11). 
BOYLE'S LAW on the variation of nronsiiro with 
volume for a constant mass of gas states that 

#v=constant (at constant tomporatura). 
Seo "Thermal .Expansion," (14) (ii.)j 
" Tliorinodynamics," g (5), (50), ' (00) ; 
"Engines, -Thermodynamics of Internal 
Combustion, " (13). 

1 Tho jibovo refoi'ciinca luivo boon SRlcRtod from a 
moro extonslve list quoted by Blcltlnaon, 



BHAKTC BLOOKS-CALORIMETRY 



.AIM-) HuidU.H,: KllKJTIONAl. lUlSIHTAXHt: OK 

HHAKI; Ih.umtH. Men " I'YidUmi," (115), 
A Vl'i IN T VIMJ Ul!' I NTH UN A I, ( !()M lUI.S'l'CON 
MNUINI:. Hen " lOnjiiiifn, 'rii(n'iii<idyitJi.nii(:H 
of liili'iciul t 'iiiiilninlioti, 11 S (-'') Il1lt ' (' r '-^) 1 
.MHMAJIT - WM I'li'.i,. Hun " UydnuilinH," 111. 

.liiuinii;, H'l'HtiNiri'ir in 1 : HXAIMI-LU 01-' KTIMA- 
THIS iii''. Hi'n " iSLnioUircfi, WU'on^tli nf," 



BltlTIBH TllKHMAI, UNIT (H.T.U.). TllO t|1l<H l " 

tity of lioal required to raino thn loin|)oral.iH'<* 

of'] 11>. of water 1" Kulir. Sen " lloal, Co" " 

diiodomif/' (2) ; "T.honiiodynainicti," S(^)- 

:il.T. 1-1 . STI-;AM "M HTHJI. Him " M1 HIM f i ' 

(if Stimm," (IN), Vol. 111. 
, Diui'TiNO, .bYANomi, AND l'Y,\rn:N ' 

INU TMHTS VOn OOCI' UK ANI> .llUA.HH 'I'lIlM^- 

fcioo " Hlfiatio Constiiiits, .DoUtrnuiiadiiiu nf/ 



C 






(tAMMIHM, NrUCJIRn [IKAT ( H' 1 , A'l 1 VAltlOUH 
j ri',nil.'i;i!A'l'iniilH ! liilinliiliHl, \viUi tlio iitcimiis 
licjU. Wri' " CuUiriiiH'try, KlcKnUimil MothodH 
nl'," S (HI), Tivliln V. 

MAUIIIWIIIN I'lHfHi'ii.TtoKrt Ki'iiiMSMAiiv m 'mn 

(IllAlHf.VTJOM III' 1 Till 1 . I'AI'll.l.AllV I'lIUK or 
A 'rHLiiMdMCTKlt. Hi'ii " 'I'lmrnioiimM-y," 

S (II) (") 

(!AU,I:SII.MI. iiitiltn- in i7 "f pULimnn 
ivditiluiH'it llH'i'iinniH'li'i', Mm rcniHliu! of 
u jnu-t-iiMiliu 1 n|ioi'inu'ii nf |)hU'imim wiv 
lirliif,; cSlrt-i'ily di-lcriiiiniul all var'nuiH 
lii-viiinvi-H 11(1' hi Uim"(J. Kon " ' 

'.L'luil'imHHiikiLH," () 
<!AIJ,r.MlMt'M KliirATION, !1,]lplU)(l ll) till) 

'iini tif Htciun ; uml 'I' 
I IT 



]<:x|ian> 

iiiH, 1 ' (Hi) ; 



i . 

OAU.MNHAII AMI HAIINKH' MKTIUID ov DKTHU- 

MININU MmiHANHtAl, KliUlVALUNT nV llKAT. 

Hen " AUidlmiiit'iil MipiiviUmiL of iltnvt," 

S(n)<l.). 

(lAM.KNIiAH AKJI NlUHLHON, .L'tl-lK!! 1 (Ill OX- 

flHiii^'n "f INVU. liolwi-cii Hltuun iinrl itylmdor 
will {Min. /''. /.<'. '--'.A'.. I H "7, iisxxi.). 



AM.CNIIAU AMI SWANN. DuLfntiiiiHtiini, liy 
Mi" iniiil-iuunim llmv nu'Uniil, r.f Mm Hiuiili 
lH .f air uiul unrlHin dioxide, at. .tn\(i- 
ul- air.tt. IHH! 100" <i Sou 
liM^rit'iil MotliodHol," (18). 
TIIWHIY, IUIMI-'OIID'H A'LTAOK ON. 
.Kniiivalouli of HonA," (I). 



<i[ luUn'iiii-l tl 
{} (UK), 'hvlilw U., .111., IV., ftiul V. 

<lAI,IIHI.MKTi:iC ! 

All iippm-iit'iiu ftn- Hut incimin-nincnb of hont 
ITin*il in nxtHTlnii'iiUi I'.V 
ji, in which M> 

l-i'iii urn mixed. S(in "<'alnn 
nif|.r\% MiiMHKl nf AUxinnV ft (R) (I.)- 

ttii'rt In* : an iiinininicnt i wldoh UK 
In-ill; Hlv.'U mil. liy 11 Iwily tHmUnK^i 11 "" 
wniut Itltftior iwmiionituro ta <.). in li 



o 



by observing t!i< ooul-raofioii \\ lii'' 1 ^ 
tivkiwt|ilticom tlioohango 1'roin iw to wiiU 1 ** 
|iro(hi(it!cl by thu liont yivnii by Um Inul^"- 
'I'lui (iliscii'vod volnmo eliaiigo in iumviTlt' 1 ' " 
into (saltn-ics by uHSiiming a vultut for tin * 
niiiHs of inorniiry drawn inln Uu> inn|,n_i 
incLiL liy tlio addition of nnn nu'im ndi't 1 ' 1 '* 
't. HDD " (Jalm'imiil.riu JlnMnn ''* 
n th Ohango of HlnLn," (i!). 
I.w,ModifloafciimH<f. St!(n7u'-/.{i^l > 
o "Conl CalorinmliiT." 

of llimsoix'fl Ten: t!m IIIHSKI "^ 
mwuury di'Rwn into Uio iiiHl-nuncnl. by (-1* 1 
nddition of ono moan imlorin nf ln'itl 
vnluoa fin mm lU'inod and l.abiilnlt'd. S*"- 
" CiUorimotrio Mollnula IwiMi-d on ll* 
OJmng of Ktatu," (S), Tallin I, 
"J)o\vn.r'H Liquid Air and llydroj;rn ; ^ ' 
liaHtiil on im aniihiK'Hitt pri n 



csijil)' to Uio stoam oaloriiiinl^i' in wliu'l* 
ono of tho liqniifii'tl nam'H in iiiii|)loyi-il it. -i 
oaloriiiititriB substiinflo. H<-(i iliiil, (H). 

DllTnronLial Steam, for 1-lic (titlorinlimt-l* 
of HpLtoifio heats of KIWI-H tit ctuilJHtt 
volume. Sco rt/d. g (fi). 

GHH. Hoo "Gas Oaloriiimtiir." 

Jnly'H Htnani : nn matt'iimi'iil in wliii-b tin' 
liouli noiifssary to raiwi tho tciupi'i'al.n* * P 
nf a liody from tho air torLiin'i'iitHnt ! 
100" m ini)auroil by dH.nrmmiiitf t-I**' 
woMht i>f atoam whioli nnmt bn (Kimlcnri*--* i 
into water at 100 to minply HUH lu-at-t . 
Hoo " Calorimoti'io MnUiodti Imm-d on I tin 
Cluuigo of State," ('(). 

Liquid. Hydrogon. Km i7nV. (K). 

Li(tul Oxygon. Sco iftM. (7). 

Motallin Blook Typ (!il ()ti Mi ' 11 " t 
JTothod of MixturoB," (i:t). 

OALOIlIMliTHA' 

OATiOiUMKTftY ia ctmocmcd with tlui nutiumt ** 
inont of energy in tho form of lifiit. 1 
(MinBtitutoa ono of tlio most illlllnnlt Imin^lM- 
of oxaob monBtiromonts owiiiK to L-' 1 " fl|t1 ' ! tttM, 
a prfot;t jiim-comlnotorof licatdot'H not o^i-n 
Tho common method of nnwuirintf mmul i 1 1* 
of luitiii in liy iitiliiiif!; the diifonvnt 
on materials such a.* tlio t' 



CALQRIMETRY, ELECTRICAL METHODS OF 



33 



temperature or the change of state, but in 
recent years another method has conic into 
extensive IIHO, known as tho Electrical Method. 
In this a definite and easily measurable amount 
of electrical energy in L-onvorted into heat, and 
the resulting change of temperature or state 
observed. Tho electrical niothud has many ad- 
vantages whon measurements of the highest pre- 
cision have to bo mado on account of the facility 
with which tho heat supply can lie controlled. 
In tho brief review given in the follow- 
ing pages tho appliances employed in heat 
measurements will bo described, and then tho 
theories which have been advanced to correlate 
the thermal data with other physical constants. 

CALOBIMIflTllY, ELECTRICAL 
METHODS OF 

(1) GrENEBAr,. The- elcoti'ical method of 
calodmotry -was first employed by Joulo with 
a view to thei determination of tho mechanical 
equivalent of heat (J). Subsequent work by 
Professors E. H. Griffiths, Schuster, Gannon, 
Callondar, and .Barnes showed that the niotliod 
was one capable of tho highest precision for tho 
determination of J. Tho article on the deter- 
mination of tlio mechanical equivalent 1 of 
heat should bo consulted for details of tho 
method aa applied to the do termination of 
heat capacity of water and its variation with 
temperature. 

In pussing it might bo mentioned thai tlio on libra- 
lion of bomb calorimeters is frequently carried out 
by oleotrieiil methods in which un equivalent amount 
of heat to that obtained in combustion is generated 
in the bomb and its amount m ensured by observations 
of tho watts diMj)ateil, the procedure being identical 
with that followed in methods for determining J, 

In specific heat determinations the great 
convenience possessed by the electrical method 
lies in tho faofc that it permits of the deter- 
mination of true specific heats, i.e. tho specific 
beat over a very narrow range oi temperature, 
and consequently it has been of immense 
service in determinations of tho variation of 
atomic heats with temperature. 
(2) Si'EOirra HEAT OF LIQUIDS HY ELECJ- 
TRIOAI* METHODS. It is obvious that any of 
the appliances which have been devised for 
tlio evaluation of J are also applicable for tho 
determination of tho specific heat of liquids, 
and further that they would give data of the 
highest order of accuracy. There are, how- 
over, certain dilficullics in practice. 

Both Callondar and Griffiths applied their 
electrical methods for thia purpose : the former 
determined tlio specific heat of mercury and the 
latter that of aniline. 

(3) SPECIFIC HEAT OF MEHODIIY. Tho 
apparatus employed by Callcndar, 3 Barnes, and 

1 Sen " Heat, Jlcimaiiienl Equivalent of." 
2 Phil. Trans, A, 1902 ; 7%s, Sev., 100?, xv. . 

VOL, I 



Cootie for tho determination of the specific 
float of mercury is shown diagram matieally in 
Fir/. 1. The calorimeter differs from that 
employed for the determination of J in that 
the (lowing mercury is the conductor in which 
heat is generated electrically and not a fine 
platinum wire stretched along tho axis ot the 
tube as in the case of the J apparatus. A 
steady stream of mercury flows through the 
fine capillary tube and is heated by a carefully 
controlled electric current. The difference of 
temperature between the inflow and outflow 
is observed by means of a differential pair of 
platinum thermometers. Tho inflow and out- 
flow tubes AB and CD are exactly similar, 
about 2 cm. internal diameter and 25 cm. 
long. They are connected by the fine flow 
tube BO of 1 mm. in bore and 1 metre in 
length, coiled up in the form of a short spiral 
2-u cm. in diameter. Tlio inflow and out- 
flow tubes are provided with two side tubes, 
one pair for convoying tho current, and the 
other pair for the mercury flow. 

A practical advantage possessed by tlio continuous 
flow method in the fact thai tho heat loss from tho 
walls can ho determined Ly making experiments 



E 1 


B 





P 


KT 



Iron Exhaust 

I'lO. 1. 



Inflow '""' EWiairat Outflow 



with different rates of flow, but keeping tho rise of 
temperature constant. 

(i.) Methods of determining tlie True Mean 
TumpEi-alure of Outflow. By far the most 
important practical detail in this method is 
the device adopted for obtaining the true 
mean temperature of tho outflowing liquid. 
If a thermometer wore merely inserted in tho 
outflow tube, leaving a .free space all round 
for the circulation of tho liquid, it is evident 
that the heated liquid would tend to (low in 
a stream along the top of tho outflow tube, 
and that the thermometer might indicate a 
temperature which had little or no relation to 
the mean temperature of tho stream. It is 
easy to malto an error of 20 per cent in this 
manner, A fairly uniform distribution of tho 
flow might be secured by malting tho space 
between tho thermometer and tho outflow 
tube very narrow. But this leads to another 
difficulty in tho case of mercury. Aa the 
space is narrowed tho electrical resistance is 
increased, and an appreciable quantity of heat, 
which cannot bo accurately estimated, is gener- 
ated in tho vicinity of tho thermometers, 

Tlio difficulty was overcome in tho mercury 
experiments by fitting tho inflow and outflow 
tubes with soft iron cylinders, em. long, 
turned to fit the tubes and bored to fit the 
thermometers. The soft iron had a eondue- 



(JAUWTMKJ:HY 



METHODS OP 



l-ivity about ton times Unit of moroury for 
both lienl and ehiiitvicity. 'I'ho honk jfoiienited 
by tlid diimmt in Um immtuliati) vicinity of 
tlio flicriuometni' hidliH wan HI> Hinnll that 
Ihn wnM-M might, fairly bn rulculalwl from fho 
iliftW<!iii!u of potential hntwi-oti HID iron bluel\H 
n(< tlio i nil Idln pi i in tn of the hi! MM. Tho 
immiury Mlnnim wan fmwd to ciixmlnlo in n 
npini.1 Miirow thread of miilnMo diiiieiisiioiiH out 
in tlio initnr Hiirfacn uf the hliuikEi, whioh 
provriited ttni formation uf Hfream-liiioH alnn^ 
ntio nil In nf 1,1 lit tuho, and Rroured uniformity 
of toniiKunlitim tb roi i(^l 1 01 it t,|io iirnHft-Htiution of 
MHI ontllow tulii', Tim hit-Si iiuiiduittivity (if 
(lui iron (lino iiHMiHkul in MCHiiiiin^ tho muno 
I'df-mll, 

A ]-m-n!ni'ly anil Infill N ilm'inn fur iivcm^inj; ilin 
uiillluw t(iiii]ii'i'jitinii A van iLjiplii'il in Clio wnlci' 
I'lilin'inuitri', Tim linlli of Ilio tlii'i'inonn-d 1 ]' \vuti 
lilli'il ivitli JL (n]i|ii'i' wli'Dvi 1 nf biuli t'oiHbiulivH.y, on 
till) Dlltttiijo (if wlliull IL rillilirr fijiil'a! U'UH ivninul (o 
111 Um unUlow tiilttt us ulii'si'ly n ]i<^Hil)lc. Tim 
iiimiinuiy nf lit wjinfi^iinl lohn nuiiili muni ini|i(ii'tiint 
In (tin I'li.'in uf wah-r tlnin in Um nimi of nmnniry, 
'1'lui ivnnoii of Iliiu i'i (InUi tlici Uii-rnml uinidiidtlvity 
(if wnlur lu-ltij( I0(r in tiinn.i li-*i Hum that of murmiry 
thn (HKiili'iitfi nvcrn^lUH of Hi niillliw Ituniicniluro 
in liiuru dcpinnli'iit mi HID mi i funnily "f Iho Hpinil 
1 ' " mill Lhn i-innjili>( cliniinatloii of any in- 



In iinliH' lo uliLaiti a porfdnl- fit fov (.lio 
- willl tlinir Hjiiml HOIDWH it \VL\H niusi'MHtuy 
([ml ilin Ixii't) of tlio oufllnu' tnhii should 1)0 ms 
nniu'ly unifurni n puMNiblo mid iHsniiriilnly 
itl.rainlili. .Id \\i\n must I'HHinitiiil that thoi-ti 
nhnuM IK; tiik iKiimU'ldtiiin ai ilm puitUfi of 
jnniil-iiMi K mul I'' with l-hn vaminui-jiutkM, 
mid thut Mm nxliH-jiiil poHiniiH nf Iho tnlicH 
jM'l, ll'l) Hluml<l not 'ID nf (tinulhu 1 hum limn 
tliy jKirUoiiH inniilo tlui viiounm-jimluii, though 
It would nut nuidor numli if Uioy wuro a littlo 



tliuiiry of Um KliininiLiidii oT tlio lutal; II>HH in 
LhoHUsiuly-llow muthoil of calorinmtry IIHMIIIIU'H 
if tlio I'loiiI'Md oui'i'iMit. mill tlwi How of 
IID HiinultiinwinHly varied in miuli a 
nuiuurr IIH En ktiop Um vim) uf lumnomljnro tlio 
HHinc, Ihw liuiifc IOHH Iiy t'lidialiun, dto., will 
mmiiiti tioiiHlimt. 'I'liii fixiiisriniontal remilts of 
('iillcnditt' mill BnniOH nlum- limb Llita 4;<>ndiU(in 
in very iilitHnly HiitiHllocl In Um mutlind, ninl they 
DiUtniiittmL till l-lui ivmillH of Uio invt!flti(?alin 
mi Uiin iinHiHii|)Uini. I'll \vnn mitiiicd, liowovor, 
Mini- Ihni-'o WIMO Hiiuill nyH(<>!iiaLie divorRoiicou 
lit Mio osjioi'iimtiihd vc'riliimlion [or tlio smull 
[loM'ii wliioli, Unmyli iiniiniiil.in unly Lo a fuw 
PUJ-IJI In HI.IKJO, ivmivfti'l (direful examination 
mi [inistilliln indlcnlionn (if (fiuiHliuil: (^rnn'H, 

Ho luiiff ii" Mix dtiitriliiitiixi <if lotnpnratuni 
llmmgliuia Um niijifiratiiH IH iincinnilitly the 
name fov Uio nanm ritio of turniu'ratnn', wliat- 
UlO flow, tllO lllt lliHH llUIHl ulu 1)0 



l. lint if thmi is any HJ-MU-I ' J V * ( ' ( 
in the toniponiliini <listril)utinti ^ s ' l 
cliangn (if How, thon thi^ro nnmt lio n i" '*'* * f 
H|)ondinj- HyalcniatUs HUTorc-imo in (In- ''*V* 
IONH, wlUisli will lead to ciitiHlant crrorii in 1' 

ciilmilatioii if no iicwiiint ifi l:nlni of it - " .. 

lioHsihlo Hinii'Cio of crrnr of tins typn in l'* ; "' ' ' 
In-ill, hy tidiidiiiition along Uio oiitllnw (i **".'''' 
Wluiii 'l.hn flow in hli'tfo, tlio liculril li'l 111 ' 
piiHftinjr aloiiH Hie. 1-idin will UtH!p il tn-nrl,y il 
a iniiffirni loinjic.raliirn, HO Unit Um j;nn I i 1 '** 
in tilts ontllinv lidio will bo Hiniill HIH I ' '*' 
iiondutition IOHH (!oiTon]i(mdin#ly initnid-. -'^ '* 
Iho ilmv JH iliininiHluul, sniiposiiiK tint lcni| " " l | jl " 
tu ixi of Iho outflow to Htmuin tlio Hiun*-. * **** 
gradient in tlio oiiUhm'-tnlio numt iiunvn^'^ l ** 
pro|iorfion to tlio n!i)iproi<nl of tho lluw, t*i'' " 
tho mdiiition IOHH i-oinuins Hourly tlm n"> |1|T "' 
Tlio mindiittlicm IOHH will vary diroc-tly iif" _ * '**" 
Hi-adiont, or invorHoly us thn llcw, for u >?** *"** 
i-ist) of loniiioratinv. 

A Hiiiallifrnirnf thin hind, duo to wmdiif* i . 
wan (lotiiotiid ut an early Htiitf in flio nn'i'-- ' ** > 
(salnriniotisr, (living to tho lar^o inaHHof mi't '* > 
in tho lluw tulio, tho Hinall rato of tlio Him' . * * * l h * 
tlio rolativoly higli thorniiil donduotivity **f r *" * 
liijiiid. It wan prnotidilly oliminati-d hy I* Hi***; 
tho ffrtMilor part of tho uiifflow tulin fro.ui * *** 
end uf tlm viioiiinn-jairliot with ]nim(Hu v*-ji -*- 
leaving only a Hinall piiHHa^o for Um on I 1 1* "** 
of iiie.ritnry. 'l.'liin niiuii) tho (iiindiKitimi I* =- -i 
vory Hinall, and nearly iiuUipendenl; f t l** + 
(low. 

(1) VACATION ow TJIK iSrKtui-'H i lh:.\ p * **-' 

MniKUlllY WITU TUMI'MUATUIIM. TIlO VilltH" "* 

tlio npenilic heat uf nienmry in teinm nf w* 1 1 * * 
wan eiiiloulated fruni tho oxponini'iifjil * I > * * " * 
tiikiiij' tho value, of .f eqniU tu -t-lKill !"* '* 
thermal unit at Ifi-fi", wliieli was tho loin j " " 
tiiro retioiiinmndiid by (irifiitliH at I hi* |'**i-* 
('lun^riwH in 1000, 

Tlio oxporiniciiliil rennltn littid tu llu* t < ^, 
prewtinn 

Hr-H-J'(l7^x ]()- fi M"(KHJHfix j() - ft (*. 



. 



Tliia givim for tho totiiporatnro otiofllott'H t 
any Uinpeintnro t tlio 



and for tho averajjo eliun^o por def-ixsi t\l ;". 
tho value - OIKKWH). 

Tlio data ubtainod in tho oxjiorinu'iit H i*r-f 
HiiininiiriHftd in Tablo L, p. 55. 

{fi) Sj'KtJiFro ll'KAi 1 OF ANIIJNK ..... 'I't-itf.-..*^^*!,. 
]']. H. flriffitliH 1 dolor mi nod tlio Hpei'ifl^ t*.*.-'.^t 
uf aniline ovor thoran^o lft to fiO ('. li.V i*r*^ tm 
of an appni'atiiH olmilar in its CHsontiiil fintt & g- a -,.. :i3 

1 I'kil. Mail., -Tan, 191)3; ftw, (Jamb. I'Jiit. ,v^ t] ,. M 
JSliC, vlll. iiart !. ' 



CALOIUMKTRY, ELECTHIOAL METHODS OJT 



TAHLI-; I 

Sl'KOU'IO IfBAT Ol 1 Ml'lUeUUY AT 
'J'l-ari'ERATUHKS 



Menu 
T c mil is rut nrc. 


S]iccill 

llfillt. 


Menu 
Tn in] ic rut. ii re. 


Specific 

Heal.. 


2 '85 


033-1 35 


32 -4 1 


033] -H 


2'93 


0334'J 


.'i(]-CT 


033 12 1 


442 


033405 


415-00 


033050 


18-37 


-033201 


53-30 


032007 


2<i-52 


03322-i 


(15-22 


032021) 


31-08 


0331 CO 


83 '89 


032818 


32 -H 


033151 







to that shown in Figs, a and of the article 
"Heat, Mechanical Equivalent of." 

For experimental work in ciilorimolry auilino him 
various points in ils favour. It Una a low vapour 
pressure lit ordiimvy tempera lures, ia a good oluclricnl 
insulator, and has a low heat capacity, 

On exposure to light it becomes discoloured, but 
no in formation is available to show whether this 
nffcals the thermal capacity. 

For the variation of tho specific heat with 
temperature Griffiths obtained tho following 
equation : 

Si-O'filBO + (*- 20) x -0004 |.((-20) 3 x -000002. 

Tho ngreomont between this formula and 
tho experimental results will bo seen from tho 
table below : 

TAIILK II 



Tom 1 Kirn turn. 


S| Experimental. 


HI .Ij'orinulii. 


1C 


5137 


0137 


20 


5155 


5100 


25 


15175 


5170 


30 


BIOS 


5108 


8G 


6221 


0231 


dO 


5244 


5244 


15 


5208 


5200 


60 


B20-4 


0201 


52 


(5304 


5305 



In tho oourso of this work it was observed 
tliat tho volume heat, i.e. tho specific heat 
multiplied by tho density, was practically con- 
stunt over tho range of tempera turn investi- 
gated as shown by tho [allowing results : 



III 



Temp ova turn. 


Specific 
Jlnnt, 


Dcnwity, 


Sxrf. 




s. 


rf. 




15 


0-5137 


1-0257 


(5200 


20 


O'filfifi 


1-0218 


020!) 


30 


-5. 1!1S 


Mil 30 


5207 


40 


0-B2-J4 


1-00-10 


5207 


00 


0-529<t , 


0' 01)05 


-5270 



(0) SwioiFia HKAT OK OILH. In Homo ox- 
porimonts in wliioh it was desired to determine 



tho specific heat of oils over a wide rtingo of 
toniporntiiro the apparatua shown below (Fig. 2) 
was employed by tho writer. 



Annular Morality 
Troughs. 

Rotating Contacts 
'to Heating Colls 




At room teinpoiuturus tho oils were ox- 
ceedingly viscous, mid eonmuniontly it was 
necessary to employ somewhat unusual 
methods of ensuring Uiat tho contents wore 
woll mixed. Tho boating noils were arranged 
in the form .of two nat paddles HO that 
they wo ro in continuous rotation through 
tho oil ; suitably disposed baffles further 
assisted tho mixing oE tho contents of tho 
calorimeter. It was nceem-iary to lead tho 
current in and out of tho calorimeter by 
means of two annular troughs of mercury 
into which uontaot bars from tho healing 
coil dipped. 

(7) 8i.>.K(jii?io HUAT OF LIQUIDS USED FOB 
llBi-'JUttBRATons. Osbom ' lias developed an 
apparatus suitable for the determination of 
specific boats and latent heats of the liquids 
commonly employed in refrigeration work, 
such as ammonia, C0 a , S0 a , m ethyl -chloride, 
and ethyl - chloride. Such determinations 
present greater experimental difficulties than 
avo mot with in work on liquids at ordinary 
pressure, since these materials have a vapour 
pressure varying from 1 to 70 atmospheres 
at tho temperatures at which tho [thermal 
properties are of importance in engineering 
work. Consequently, in tho design of appa- 
ratus for experiments of this character great 
attention 1ms to bo paid to details of con- 
struction. 

(i.) The Calorimeter. Briefly the arrange- 

1 Jltill. .iitti: SMa., 1017, xv. m. 



OALORBtETRY, ELISCTBTCAL METHODS OV 



mmit i as follows : Tins matoriEil to lw investi- 
gated i isnelosod in a calorimeter with thick 
molnllio walls of known thermal capacity 
([''iff, it). H'diit in applied (?leotrically and tlio 
jiu'Jaifc IN maintained tit tho same temperature 
by MIC umial adiiibiiLin firmiigoinont. 

An uir HHIUSO between the polished nickel 
HurfjusiiH uf eiiloriinotw and junket furnishes 
tlwirniiiL inmihition, Two tiibcn oxtoml from 
fcln> Lu]i u[ {,ho (mlorimotor through tlio jacket 
and Him id to tlio outside air, terminating in 
VOJVOH. OIKS of tlieao tubes is intended for 
uoiiiuMiUou to prc&aiiro-iudicating apparatus 
and Hie other for tlio introduction anil removal 
of tlio nifltorinl to bo investigated. 

Cum \VIIH 1 n!t i>n to nviilil having heavy metal 
oojini;(iliot)H nuiort!) l!i<> uii' Hpnco mid by suitably 



-Supporting 
Ring 




- Copper 
Envelope 

Cooling 
' Ring 



JNo. !i. HccLliMJ oE Calorimeter audJaokcl], 

dJtitHbiiting Ihoso coiiiinoUoim which arc nccoasfu-y 
ovor tho onlimtnolor surface, tlio part of tlio 
llipi'jiinl IwiUiigo tine la lend <jomluolion wns consider- 
ii My jmniinluod, Tlioi'Jiiooloinctila indicate rotative 
Hiirfaco lompcrniliirca o( tlio jacket onlorimctcr, 10 
jtuiotloiiB boing illfttributcd ujion cnoli surfnoo. TJiia 
pormltB of control over the thermal lonltngo and 
t!io uorreislioii for Hiioh lonltngo as could not bo 
uvfjiilod. 

Tlicnnojiinolldiia plnceil upon Hio connecting tulica 
imllcftio tlin tomni^mtni-o of llioao tuliM at sovoral 
\m\ni-n tvliulircs lo rt ]ioitit <m HLO jnoltot and in this 
\viiy MIC tiiinj)ori(tnni of Uw vuponr oxpollctl during 
Vdjini'Inalioii nxjH'i'i'mitnlj) could bo found. 

ILlin Iiifdiln f HID ^cntml tulwin tho oalorimotoi' is 
iioocNBlhlo at Uni ln)l,Uim for llin introduction of tho 
hcnUiitf coil and tfLcrniomiitor. Upon tlio o(*ido 
of thin tuho nro fa^toncd 12 mdtiu vanca of tinned 



*' J " 



* * ' 









* " h ' 



iron alioiit 0-3 nun. thick, extending to wilhiii "",,"*.. , D . 

1 mm. of (ho surrounding cylindrical wall. *- J -, t , 
vanes nro for tho purpose of promoting th\ '." 
(.rihufion of heafc within the annular space eon 1 * * ' M ' * . 
the nmloriul uiulor investigation. Tho vaiie.H i 1 "* " ' "* 
just above tho top of the central tuho. At I hi" I 

are two flat circular bailie plute.s, soparal)'<l ** 

2 mm. by tlireo Hinull steel studs. The lower ] > 1 ' * 
uniled to tlio tops of tho radial vnnca with til*- 
central hole in tho lower plato and several Ii" '"' 
tho upper one between centre- and oul.sidi* f* 11 
a tortuous pnsgngo for vapour coming from I M 
These two plates aro intended to inleiTC|>l" 
large drops of liquid which might bo thrown lt l 
vigorous boiling, should it occur, and also iiml* 
thermal shield for tho top of tho caloriuu't* "' 
second wot of four bafilo plates of nplwiel < 
separated by about 2 mm. aro attnohed lo thi' 
fiiii'faco of tho conical part of tho calorlmctfi" c ' 
Each plftto has a central hole and four ulntu *-* 
edge so ns to avoid trapping gas or liquid, lmt- * * l 
passages are so sized and spaced that the um III. !' 
through tho plates is very tortuous, BO an to i* 11 
difficult the passage of liquid partielen from t>*'^ 
in a current of vapour being withdrawn I In 1 ** 11 
the outlets in tho top. Tho entire inner mirf!*'" 1 * 
tho steel shell and of tlio various plates wilJih* "' 
all tinned, using puro hloolt tin. 

(ii.) Method of Experiment. Two Uinlii 
methods of experiment wore employ im I 
tho first method tho heat, added to u. tif> 
amount of tho auliatnnco uiulor test (imiUr 
in the calorimeter under saturation comlit -i 
together with tho resulting ohatiffo ill- * *' 
porature, arc measured. By using ilitt t. 
tho specific volumes of tho two phason mi*l 
latent heat of vaporisation, tho heat !**>*< 
tho vaporisation of tho liquid is 
and can ho allowed for ; thus tho 
heat of tho liquid when kept satunit'*l l p 
found. 

In tho second method tho onlm'iui(^i*r i'* 
kept full of liquid at a constant iirt'Hun '. 
The heat, added to tho variable amount ii t t 1 1*' 
calorimeter, and tho resulting clwngii in l*'(*i- 
pora turo aro meamircd. A coiTCotion {* t* tlm 
heat withdrawn in tho expelled liquid IH * I<?1 '!.'- 
mined hy special oxpoiiments. By im< *t t lu 
data for variation with pressure of tln> Jnt**i[, 
heat of tho liquid, obtained from Jiojnuvilo 
measurements, made with the same uj>}un *it ir>i 
and material, the corrcotiona for |>rt"i;t.nti \~f 
variation aro applied, and thus a- m*ij< ml 
determination of tho specific heat *tf 
saturated liquid is obtained. 

Aa a final result, tho apcoifio heat a, In j 
per gram per degree centigrade, tif 
ammonia, kept saturated, at tho tom]H>v*it.m.t' 
0, is given in tho range -45 to -Hfi w c\ ly 
tlio equation 



* " * ' 



' '' 



*,M ' " 



* J1 



f "' 



ff 

Tlio two curves in l^ig, 4 show tho 
graphically. 



CALORTMETRY, ELECTRICAL METHODS OF 



37 



S) Si'Eortfio HHATH oir SOLIDS BY. KLUC- 

^T, METHODS. Very little work lias boon 

on tho determination of tho specific heat 



heats of tho motala aluminium, tin, copper, 
cadmium, zinc, load, and silver over tho 
range -160 to + 100 0. 



I 

Specific Heat Liquid Ammoni 

Upper Gurus- ni constant pressure 
equal to saturation pressure 
> QbsatuotI Points 
Lower Gtirue- at saturation condltloi 
Mean Equation ff=3>!3GB-0-OQ0570+f= 
o Observed Points - Ftrat Metl ad V ' w 
x a ii Soeontl 












/ 


3 




Const 


nt prcssw 

/ 


,/ * 

/ Z 
' S^St 


/ 

(lira (/on 


4* 
~0 




./, 


& 

^ 















^ 


/^ 
&* 


^ 














^ 

<^^ 
^ 


^<* 

,<*r 












^ 


*** 


^ 




Degrees 


0. 











lid substancea by tho electrical method 
it lor tho metals. The- method, of course, 

itself admirably to tho determination of 
jjooiflo hcata of good thermal conductors, 
vitli poor conductors special devices nuiHt 
lopted to ensure uniformity of tompora- 
fcliroughout tho material under test. 
3) GAEDR. Gacde l appoara to Jmvo been 
first to measure specific heats in this 
lor. In his experiments tho specimens 
3d their own calorimeters. Those wore 
.tiled to a cylindrical form and a deep 
nl core bored out. Into this was thrust 
pjier core, wound with a properly in- 
3tl heater of oonstantan ribbon and a 
anco thermometer of fine copper wire. 
:iial contact between the core and the 

of tho well was secured by filling tho 

ironing space with mercury, using a thin 

shell when, necessary to avoid amalgama- 

TJiis calorimeter was suspended in a 

.lostat and heated through an accurately 

tired temperature interval of about lfi a 

measured quantity of energy supplied 

i-ically. 

vy few particulars of the investigation 

been published, and tho data obtained 
.immarised in Table IV. 
LO) METALS. Professor E, II. Griffiths 
Dr. Ezor Griffiths studied a tho specific 

fi'ljs- Zcitschr., 1002, Iv. 

ftil. Trans, Hoy. Soe. A, BOO. 10J3, ccxlii. 110 ; 
?oc. Froo. A, 1014, Ixxxlx. GOl ; Phil, Tram. A, 
-OH, p. 310. 



TAIII.I; IV 



MimouiiY. 


I'JiATIXt. 


STEEt. 


I'ouiljiim. 
Into, 


Bpcolllo 
Heat. 


Tuinpoiw 
tre. 


Hprnino 
limit. 


Tern peril 
tun. 


HpcoLflo 
Heat. 


17-1 


03320 


17-C 


03128 


lfl-8 


10M 


31-8 


03311 


32-0 


03140 


313 '3 


1082 


47-2 


03302 


47-8 


03107 


47-1 


10UI) 


Ol'O 


03202- 


02'2 


03180 


02 '0 


1114 


77-0 


03282 


77 '2 


0.1103 


70'7 


1120 


02-0 


03273 


92-2 


03205 


01-0 


1144 


LEAD. 


Asa'iMONir. 


TIN. 


I'ompern- 
turu. 


Specific 
H&it, 


Touiinmi- 
lurc. 


S]iOc!flo 
Jtcnt. 

0502fi 


To in porn - 
turn. 


Succlflo 
I [cut. 


18-3 


03054 


17-1 


Ifl'8 


05308 


32-3 


0307fi 


33'0 


050fiO 


32 -B 


Oli'HO 


47-1 


03091 


47-2 


05082 


40'8 


055 J 80 


01-0 


03103 


02-4 


05103 


02-1 


05534 


70-0 


03112 


77-3 


05110 


7(1 '0 


05580 


02-0 


0312G 


02-5 


05132 


02'1 


OG5023 


ZINO. 


CADMIUM. 


OOPPHB. 


rot!i]iorn- 
liim. 


BiMoino 

Hent, 


Tompom- 
tum. 


Sjicc Ilia 
Heat. 


Tomporn- 

tlll'O, 


RncMa 
Hcnt, 


17-3 


0022 


17-1 


OS483 


lfl-7 


0011 


324 


0020 


32-2 


Offi53fi 


32-7 


0010 


47-2 


0030 


47-1 


OB500 


47-0 


0024 


02-2 


0041 


01 >8 


05504 


01-0 


0031 


77 -3 


WHO 


7fl.fl 


05029 


70 '4 


0035 


02'7 


0940 


02-2 


00055 


92 -3 


OD'10 



THY, KL'KCTHTCiAL MimiO'DS 



(\.) Twiipwaluren IV'. 1 00".- -TJio nppaml.iiH 
cmployi'il fin 1 (lolitniiiimlionfi in thn nuijfo 0" 
tit lOll" 0. m nluiwn in Fiff, fi, 

Two ittmilivr liliwliN uE thn nintnl under fr.nl. 
M'uri' iniH|)i'iuli'<l in two limns Miiiliwnri'it im- 




.Kici. 5. 

iti a nmmliuil loin [JowLim* batli. in 
llir (icmlral liolu n[ cimli MnoU mm a 
t]i ill \vliilnt Lbn tioiixlnl hole" omitiiinud 



. 

'J)lio Uiifd hnld WHH iihwl for llio jmi-puHo ot 
Mui hltiiik ImliMV Lhi* Hnmninilinn loni- 
liy llio irwM-Linn of u l-liin-millril tutu* 
iiij.; ol-lmr innl ()(iniiii(il.inl In n walwr 
piinijj, 

In Mm i'X|jii'lnicntN oim nf Hio lilontiH WRH 
ItimUitl Uiron^li u nuiMi' fi""'" "i" 1 iJt'Ki 1 *'*' I'l'lnw 
1-1 in lt>]ilin | <ruluw nT Un <iii'liiiirn Lit oim ilfjfivo 
iiljiivii llni ImuimniUiHi of Lin' oiiisliiHiim ly a 
iiiiiHHumd tmiii'ly >r cli'oiviiuil c-iH'i-^y, 

Tltw tf>]ii|n>nvLiii' Inlrrviil AVIIH iiiuiiHiinHl on 
ti ronSMiiuiiKi l'i<lno in Um imiuil mitniior. Kitmo 
Mm \t\vit rcMiHlanoo t]Hnnnmotcrrt woro tidjimttnl 
t.n oliiKo o(|uulil,v imd iiuulo of llio HiinK) muiuilo 
nf wiro, U* ImlaiKiii jinhvli on Llin lii'lilgo \vii-n 
\vH |>nit)tioiiH.v ill llio cniili'P of llio wlvo al 
nil Lnm|i(inilim-H wlion llio liliidkfi woro in 
liMnjicrnhtro ni|iiililiriiini willi Um wmhiHurc. 
llt'iino no imsilliiry titill wen* rw|iiiroil in tlvn 
M'lJiMifHlinio'H luidKO dirmiit linyniul l-ho c<inu! 
iutlo HITIIH, 

TJio oiini^y Hii|)iiliml to tlto limiting coils WH 
inoftaumil ly ImlimuliiK Um iiotcnLinl difCoronco 
lit lift uiitln nKftliiHb tlio I'l.WVh 1 . nf a norloH of 
oclla hi aodon, Llio ourronl. tlmmtfh tlw 



noil boing ndjimlcd iniLil balmnso was nlit i* 1 ' 
Tlii) ri'siHtuntio of Uiu b^utiny uoil WIIH "*" 



tit 



in, ,i t i 

ii.) Low Tf.m-iifmlurf.it. Tlio oxjtovi **" .' 
worts isimlinwsd ni low toiniujrutui'tiH but- p ^* , 
a niodifiml form of <ip|mnitiiH slmwn in /'*' '** *' 
an il^ wan very dill'iimlt t,n obttiiii nny "<*' ll * ,'!*** 

" * 



' 1 V 11 11 
!>>' > 

1 " "' 



*''' 



-mr<!. 

hi Una (ippnratiifl u (sonstant 

iimilosiiKs wna obltiiniHl liy tins IIHH of si 

walled (Hipp 

coil of 



eoolod all- 
lutwl. Tin 



1*1 il 



iHod in a. * * l * 

inaiini!! 1 . A i ' ^ l! " 

l!Oinpl't'H!U'<l * * ' M 

, f ^ M M * 

to DOIH) HJH. r-'t 
w[. in., ii J l IH-H 
onltiri'd iiil * * * *"' 
i'liaii|;<-i" _ ''>' 
/ipi 1 A, /**?!' (1 
ThiH inU't'.-1t*tt ( -' ' 
lilt wan *' " *|- 
alriu'.lod nT * mil- 




miry solid drawn copper tubing ft In, | 
ooiloil in Llio form of llaL HirU. 
oosflivo laj'oi'8 of tlio coil worn Hcpnrettful 
etripa of oardboard and tlio ontiro coi\ itn^ 



CALORIMETBY, ELECTRICAL METHODS OH? 



around will* heat-himilaling material. From 
the i n torts litnigor coils tho air was carried to tlio 
valve G, by moans f which nn observer Con- 
trolled Uvo Hv, excess of air being discharged 
at tho Hafuty-valvo on the eomprcHsnr. After 
expansion tho nir circulated through the coil 
of lend tubing A and then back over the 
surface oi tho interchange! 1 coils. On the 
exterior mititieo of tho thick-walled copper 
enclosure I'j wii9 wound a layer of insulated 
copper wiro .I 1 ', whUili served as a rests tnnco 
thermometer. Variations in tlio temperature 
of tho walls of tlim enclosure were rendered 
visible by the movements of a galvanometer 
spot. .By ' controlling tho flow of air tho 
oaeillatiiHiM of tho spot could bo kept within 
narrow limits and, inidor normal conditions, 
the oscillations did not exceed a hundredth of 
a dcgrco in. amplitude, 

Tlio intuL'ior of tlio wooden vessel M was 
packed with ulag wool, 1 tho passage for tho 
withdrawal of tho copper enclosure being kept 
cleat- by a cylindrical tube of cardboard N. 
'JL'ho space between tho top of tho onclos 
lire and tho outer lid was filled by wrap- 
ping felt inntting around tho glass tubes and 
leads. 

Tho blooli of mottil G was suspended within 
tho enclomiro by a single glass tube H. The 
eontre liolo uontaincd the heating coil 0, of 
manganm wire wound on a mica rack and 
immersed in. a light, pnraflin, usually petrol. 
Tho boating coil -was fixed to a short taper 
ping of copper K, wliich cloned tho eontrat 
hole. '.I'bo ruHintanoo of tho coil was about 20 
olmiH, A platinum thermometer was inserted 
in tho cylindrical hole T, tho annular gap 
between tho stem and tho walls being closed by 
a packing of nshi'sloa thread. Tlio differential 
arrangement employed in tho previous experi- 
ments WHS abandoned ns it would have required 
too long n time to obtain tlio equilibrium 
conditions. 

(iii.) Method nf flayer iment. In these experi- 
ments thu practice- was to heat tlio material 
through u Hinall temperature interval from 
below the mi rroun dingo to an approximately 
equal iiitorvtil aboyo f and observe tho rate 
of rise chiving this period. Tho method of 
experiment; was such that a direct deter- 
mination of tlio temperature of tho enclosure 
was not required. An experiment was con- 
ducted o.s follows : 

Tim tcmpemtm'o of tho enclosure was lowered 
progressively by utiliHing Hie full supply from tho 
compressor imil controlling tho How so as to produce 
a steady prcanuro drop through Uio valve of 120 to 
IfiO aimcKnihei'CH. 

Tlio tumpcmture. of Uic block would fall at a steady 
rate by radiation nd convection to the enclosure 

1 It la prohnblo that wool In Ua nntnrnl stato would 
liavo lifion it better Itwnlnlor at those low lenrnera- 
tiircB, shuwi ilin fireaHO In tho wool prevents It from 
absorbing moisture. 



wollH, and whon il.i tempera turn liad nearly readied 
tin; desired point the euld air circulation around tlio 
cjicloHiii't* was Blopjicd. 

Its tern pern turn woidd then rise rapidly by 
con il notion from without and BOOH pass that o{ the 
block which, in consequence of tho slow trull Km fusion 
of licat by radiation and cnnveotiou, would lag 
behind that of tlio walls, Tho lomporaturo of tho 
cnolosiiro walls would then bo niiiintiuncd nlcady at 
about threo degrees higher tlitin that of the metal 
block. 

Some time had to elapse before tlio conditions wore 
Biiflicionlly settled to jimUfy tho ooiiimonconiciit of 
an experiment. 

The lir.-ifc group of readings connisted of observa- 
UOHH of tlio rule of rise of lcmpcrn.turo of tho blnolc 
by ratlin tion, etc., tlio trannils of tho loiniiovatiire 
being observed across HiicoeH.sivo equal intervals 
(of about ij'jjlh of 11 degree), tho time hotivcon HIIO- 
cesHive transits being of tho order of fiO Koeonda, 

The electrical supply waw then nwilolied on, and, 
after allowing a little time for tho sotting up of a 
steady gradient, transits every fifth of n degree were 
(niton. 

Wlion tho temperature hud risen two or throo 
degrees auovo Iho HiirrounilingH tint electrical supply 
WUH switched off and observalioiiH of (onrpcrnturc and 
time continued. 

The tcm]):iraturc would then fall steadily under the 
influence of radiation, etc., tho rate of cooling buing 
olwerveil in pmoinely tin; same manner us Iho rate 
of rise of temperature before the electrical supply 
was switched on. 

If <j in the rnto of rise or fall due to radiation 
for 1 C. dilToronco in toinjioratnro hetweon tho 
block and tho Hurrouiulinga, then assuming 
Kowton's law to he valid for tho loss or gain by 
" radiation " (an assumption which was fully 
justified by tho experimental results), wo have 
tlio oxprefisicm 



for tho rate of rise or fall under tlio influence 
of " radiation " nlone. Hence, plotting dOjt)t 
against 0, tho straight lino joining the two 
groups will out the temperature axis at = 
which determines tho temperature of tho 
aurroundingti. 

.for the rate of rise under tho combined 
effect of tho eleetrieal supply and radiation wo 
have tho equation 



where E a /Il is tho electrical supply per Rooond 
in thermal units, MS tho thermal eapaeity 
of tho bloclc including that of tho resistance 
coil, etc, 

Plotting tlio observed rates of rise on the 
Btinio scale as tho " radiation " observations, it 
is obvious that tho straight lino thus obtained 
should bo parallel to tho lino joining tho two 
groups of " radiation " observations, since tho 
tangent of tho angle made with tho axis is 
equal to tr, For = tlio " radiation " term 



10 



KLEOTRICIAL METHODS OF 



vtmmlu'N, honco, if D(?N/(")(. donotos tho value of 
the ordinato at this ])<>int, then 

< 3fl .K~ W 

' tJi iuiw 

from which & can ho oblnincd. Tho results 
obtained avo MiimmaiiHcd in Tablo V, an<l shown 
in /''(';/. 7, whoro T is the absolute 



(1--2 
Q-O 

fi-G 

0'4 

y o-a 

111 

-Co-o 

04-0 




TYio ialtar H donotea tb& absei nations 
of Hamst In ilia onto of allwr mul of 
la a it. 

0Ceaf. WOOent. 

Absolute ', Temparnliiro \ 



100 



1UO" 2SO U GQO 300 QflD" 3QO 

l''IU. 7. 



loinjjoraturo and ('! is tho atomic lioat, i.e. 
heal- miiltipliod by the atomic weight : 



TABLI-I V 



Alls, Spnclfln 
Tflinti, Ifwit. 


cv 


Alis. 

'L'(!1M|>, 


Siicclflc 
JliuLt;, 


0,,, 


C'Ol'I'KH 


IDS 


0-077(K1 


4-W 


301-0 


0-00230 


fi-87' 


140 -fi 


0-07IM2 


ri-ofi 


sail -7 


0'0l)30fi 


fi'iiri 


171-4 


0-08235 


ri-2!) 


a-Ki-fi 


0'0l);i87 


5-1)7 


2IM-I) 


0-OK503 


ffll! 


370-li 


0.00521 


(1-Ofi 


273-1 


0-ODOBH 


rt-78 






.. 


HlNCl 


MB'li 


0'08'I2] 


fi-fiO 


32S'(1 


0-00112 


0-15 


21J-1 


O'OKKOH 


r.82 


370 -fi 


o-oonsi 


0-22 


2711 -1 


0-1)1117(1 


-00 


3011-fi 


O'Oiimo 


0-20 


20-1-0 


O-OOLMft 


-00 


.. 






-Klf.VKIl 


IfiH-l 


o-osaio 


fi-fl2 


301 -5 


0-05013 


fl-ofi 


187-4 


It-l 1.131(2 


fi-78 


:i-io-r> 


o-onoso 


8-13 


273-1 


0-OB5fSO 


-00 


370-0 


0-05737 


0-19 


(AVUMIOM 


IOH.;I 


0-04007 


B-fi2 


noi-fi 


O-OGfifi-i 


0-24 


IS 1-8 


0-M2B7 


fi-0'1- 


327-0 


0-OD01 


0-31 


273-1 


QWvMR 


0-16 


370-8 


0-057 14 


n-'iz 


LKAW 


llft-41 


0-028(17 


5-04 


301 -5 


o-oaofi;i 


0-H2 


liM'S 


-0200,1 


0-01 


32-1 -1 


0-03073 


0-30 


2fi-I-l 


0-02080 


(3 -11) 


MO-fi 


0-03102 


0-J2 


273-1 


0-031)20 


(J-2R 


370-fl 


0-031137 


0-d8 


fiOIIIUM (AsSHAIiEl)) 


ia'i-3 


0-LMWJ 


5-117 


>r.\-i 


0'2H2D 


0-51 


lflfi-2 


(t-2fif)ll 


fl-tlfi 


3(W-I) 


ft-2010 


(I -HO 


i7it-;i 


0-21 111) 


ft -02 


il22-l 


0-2!lfi2 


(i-70 


2)0-5 


0-2707 


(l-2il 


3JO-0 


0-.1010 


(1-0-t 


270-0 


0-282^ 


n-ni 









TAHLE V cotttinwtl 



llcafc. 



I H 



( 't ' 



fioniiiM (MOLTEN STATE) 



300-1 



0-3234 



0-3217 



7-H 



7 !() 



4-1 Ml 



0-31HU 



g (11) NEUNST AND 
ohsorvers made a Horiea of point to point il< ' '--** 1 '" 
minations at very low tonipornturoH, imii**' Jt 
calorimeter developed by Euekon. 3 A im****' '' " 
metal of suitable ai/.o was shaped into u lie *i ' * * w 
cylinder and a loosely fitting core miulei fui' t-' 11 * 
same. On the core was wrapped a plulii"*" M1 
wire, properly insulated, to serve as a ruHmtJi-t " '''' 
thermomotor and also as olootrio lioator, 
core was placed in tlio cylinder and 
poured into the crevices to improve tho 
contaot (see Pig. 8). Tho whole was Himptit i * I* 
in vnctio, and tho speoilio heat ovor i-*i'" 
tomporatiiro intervals 
detorminod from mensnro- 
inonts of energy supplied 
electrically and of tho 
tomporatura rise roflulling 
therefrom. Nornut ami 
Lindomann applied the 
same method to poor 
heat conductors. For 
such materials the design 
of calorimeter is shown in 
Jfig. 9. Tlio wire was 
wound on a silver lube 
projecting into a silver 
vessel, tho high conduc- 
tivity of tho silver assist- 
ing tho equalisation of [,-!, 
tho temperature through 
the mass. Some of tho data ; 
rnotals obtained by Noimt aro 
TahloVI. ' 

(12) OoH'iiii, Harper a stndiod 
specific lioafc of copper over tho range 
16 to 50 t!. Tho specimen was in. 
tho form of copper wire, which a]m> 
served ns its own tiiormoinotor and 
lioator. Tho wire was fiO metres in 
length and- 2-5 mm. in diameter ; it 
was compactly coiled into n number 
of Hat spirals separated hy mion, 
plates. Tho ooil was suspended in 
vacua, and heated with a measured ,. 
quantity of energy supplied elec- 
trically, tho rcanlthig temperature HHO l 
measured hy tho change of resistance. ' 



H. 



U 



1 Jotirn. tie PhuHiqw. 1010, [-1], Ix. ; Silguuff 
llcrl.^Al-atl 1010, I. 247, 202 ; Ann. </. 7*fty*., I 

*' PhusA; Zeitschr., 1000, x, (J8fl, 

1 Sci, Paper Hitr. SMB., 1014, No, 231. 



CALORBTETRY, ELECTRICAL METHODS GIT 



results of 27 determinations butwcon Ifi and 
fiO uro represented by tho equation 

S = 0'0917 + 0-0000!8(f- 25) calorie^ ]r 

grain degree. 
4-182 joules is taken as n<[iml lo <mu 20 calorie. 

(ii.) Comparison a/ Data !>// Varioun Ob- 
36i- vers. liar per 1 lias tubulated tho data given 
by various observers for tbo HpceHIo bout of 
copper. In order to compare the results at one 
definite temperature tho coefficient (M)00(M4 
has been used in reducing results obtained at 



This eocllioicnl is l!u? menu of Ihcisn u'nen liy 
recent olwoi'viT.s employing isloelrio luiiliug jnul a 
jioinl lo [mint mettiml <IH shown in Tiiblc Vll. 

TABLB VIC 



Observer. 



K Jl. Orimtlin ond\ 
K/er (JriDHlis j 
Harper .... 



Cnlorlra pin 1 (li'iijn I Ji' 



0-<10fK>H) 
O-OOOO-H 
0-000(|.|K 



TAIII.I; VI 
NEKHST'S VALUES AT Low TEMPHIUTUREH 





T. 


;t2"i 


3r ( 'l" 


H;) 


8C> 


88.3 






Al 


% 


0-25 


O'S, 1 ! 


2-11 


2-f2 


2-02 








T. 


23 -B" 


27 -7 


33 -4 


87 


88 






Cu 


c s . 


0-22 


0'32 


0-04 


3-3, 1 ! 


3-38 








T. 


dO 


GO" 


80 










Zn* 


CP 


1'77 


3-lfi 


4-00 












T. 


35" 


3!)'1 


44-2" 


52-0" 


Clfi" 


77 


8.1-3 


Ag 


UP 


1-58 


1-W 


2-:if) 


2-S5 


3 '74 


4. -07 


4-37 




T. 


23 


28 3 


37 , 1 ) 


80 








I'b 


^ 


2-OB 


3-02 


441 


fi-(!0 









It will bn CI|).MOI L VIM] from 
a ooinpiirifKHi of (lio datit 
gtvon in '1'ablo VI11. (p, 
42) nnil wlimvn griiiiliuinlly 
iu Fiff, W tlmt Llioro in 



tho rc'siills iE 
observers iialng tho oleu- 
trioal jnoilind both as ro- 
gards tlio obsohilo valuu 
of the H|icoifio Iioat and itn 
toinpovatiiirt! coofliiiioiit. It 
ia very iinprobubHo Unit 
thoro in any ByHUstnutio 
ort'or common to nil HIIICKV 
the tliroo inotluuls clifim 1 
nidieally iu (Jdtnil. 
(13) KI-IXIILMO HMAT 

OF CiAHlIH JIY El. 

Tlio 



. T ,, , of olcubiiuiU hontintf fur 

111 !', ho . (;aH P " f ? lll l] !. "-."'"I 11 . "* " <)C Mirilinl L ima Urn aliovo t ], clotoriiilnialun if tlio 



, 
liBiires litivo iJOfin obttiineil from th tsurvcs given In tlio pnpcr. 



tho various lorapomturea to tho fiO 0. value, 



tlio foi'jinita 



S = So i- 0-000044* 



Hpeoifio heal of 



at 



diftoront tempera-hires 1ms IHJOII dovolupwl by 
Callondar and liia nssooiatL>a. 
Gases present grontor practical tlLfliouUios 



100 ito" iarf tad 1 



O'OOQ -5 




001 =- 



o-ooo -s- 



-20 -10 o 3 10 za> ;io 10 DO" DO" 70 ao 00 100 no' 
Fro. 10. R]ii!Dino Ilpivfc of Copper. 



boing nasumod us valid for valuer ()I ( from 
to 100. 

1 Set. 1'ajier Jiur, Stits., 1014, No. 231. 



than either solids or liquids, since it in nocrsHiuy 
to tdko grout prcoaiiticMia tn oimuro 
of tomjiorature in tho gim 



OALOniMKTKY, ISLEC'RUOAL METHODS OF 



'L'.uir.K VIII caulinued 











Ulle. 


Von r. 


Name. 


Temp. 


It (Will, 


Vuhii! 










at ftO" J . 


1010 


MngmiH 


!/>.]( 10 


o-oim 


o-oos,, 







)fi-a:i 


0-OOtl 10 








]Ji.;t:!8 


0-0',)i)7r> 




1010 


Jtiolmrda mul Jnokson 


~ 11)0-20 


0-07811 




1010 


iS oil imp 11' 


- 11)0-17 


0-0780 






H 


-71)-] 7 


0-0880 








17-100 


0-0025 


0-01)2 


1010 


Ncrnsl, Koref, Limlinnann 


2. 02 


04)0 lffi 


0-011:12 


1011 


Koref 


- ti)i).H:i 


0-0720 








-77-0 


0-0870 




3011 


NoniBl nwl Iihiclonmim 


- '>;t:r 


O-Ol^ 






.1 .. 


-213 


0-020, 






>i ii 


- 103 


0-0 Illj 






X l> 


- 17 


0-0f)0 




1911 


Nuriibb 


-249-0 


o-ooaii 








-2>I5"1 


0-0051 


, , 






-239-7 


0-0081 


, , 






-18(1-1 


0-OM 


, . 






-18G-1 


0-OB3 


, , 


1013 


fir/filths and OriffiUm 





0-011088 


0-ODftl 






28-4" 


0-09230 


0-00:12 






07 -B 


-00:187 


0-00:11 







1)7-4 


o-oor>2i 


0-Oim 


1014 


Harper 


Ifi.fiO 





0-0(121) 



20" cnloi'Io, hydrogen ncnlo. 
Coppnr 09 -ill JUT font puto. 
<>\]triwa<Ml in fnviiuiliv 



liivio (jqunl Hi 4-1 SB jmilcH. 
\Comiii( i roial drawn copjipr. Caloric 
J oiiiuil t(i 'J-lfifi jmilcH. 
Ciiloi-io prpial to 4-188 joules. 



(Assuming ico-poiiit=273'lIC.) 
! Elt'olroly tio copper. In IcniiH of n 
onlorie equal to -J.-18S joulca. 

Very pure clend-olyl io ooppcr. .ISIeotrlo 
hcfiliiig, point U> point method, 

HuHulls ivxprcNSisd l>y fonnnla 
c-0-flt)l)fifi (l-t-O-OOOfiS'iU- 0-CVIHJ 5 ) 

Kcsiiills ('xpri'Kscd ly formula 



Thu unlta In terms of which tlui ahovu results avo oxnressiiHl uro not all (U sumi!, hut tliti illlforaii'iM nncil HOI 
ho tnliea Into luiooiint In maklns eomimvisoim. In overj' oaso the illfforonuu between the unit employed anil 
the 15" euloiio or tho 30 eulorlo (whloli illlYor from each othor by about one, imrl In * Ihouanml) In lens Mian (ho 

cooled. Tliia i.ulio was packed with tightly 
Jitting discs of <n>ppor gan/,o. Tho gas under 
test entered at m, was heated up to tlio required 
temperature and entered tlio spaoo round llio 



Otillomliir and Swnim 1 ap])Iii!(l tho oontiini- 
ous (low inotliotl to tho dctoriniimlioii o tho 
specific lionts of air and onrbim dioxitlo at 
atmospiioro pressure at 20 0. A 
and 100 0. 



SJli- 



(i.) f'lie Ap]xtmls. In those 
oxporimonla a steady stroiun 
o gas was passed through a 
jaokoted tube (tho eiilmimctor 
proper), in wliich it was heated 
by a current o( elcotrieity paa- 
ing through a platinum coil of 
1 ohm resistance, tho rise in 
temperature being measured by 
two 12-oiim platinum tliermo- 
motors used differentially. 

Tho calorimeter is repre- 
sented ditigrainmatioftlly in 11 B " ri 
/''((/, 11, tho hooting ooil and ' [<1 ' 
platinum thormomotors being situated in tho 
tube AB, which in jaokoted by Ibo tube it, Thu 
tube FGt formed the heator iiv whioh tho gna 
attained tlio desired tompoiuLuro, and boing 
double-walled could bo steam-boated or water- 

1 Phil, Trans. A, 10 10, uex. HH), 




i nllow exi'csH nf |ian to CKCIII.WJ lilt, 
contnlnlnR milli! K01E anil <'a(!l a ; l!, cutliHi wool ilniiL 
filter; I), luitoinatln jirwmiro KUiilaUii 1 ; I 1 ',, throttld: 
F, lunci mckeil wllli BOIIKO to lirhw HUH to tlia UeHlruil 
l,n i n lie rn tuns ; <), fluo molnl tuln'S for mcnKtiroinotit of 
How; 51, ollKaiif(, 

cnlnrinictor propoi 1 . It next puBaotl through 
the tubo ?i, into tho ealurimotor, and finally 
emerged by tho tube p. 

Tho general ixiTftugonient nf tlio 
will bo undo] 'stood from Fig, 12. 



4.1 



CALOMMKTRY, ELECTRICAL METHODS OF 



(ii,) Theory itf MctM.W (! is t!io clrctmi current. 
.K tlio potential (lilformu'Q between I ho rauln of the 
heating coil, SW (ho rinn in temp Mature of the gas, Q 
I ho rnto of llmv of the gas in grammes per second, ,1 
tho mnclinnitsiil equivalent. nf heal, nnil 8 the specific 
heat of the gns at cons tout piTRanro, tho elementary 
theory of tlio espnriment gives 



ivhoro ft30 IN a term representing tlio heat loss by 
radiation, etc. 

A similar experiment with a rato of How about 
bait the nbovo vnliin, and witli Uio clcolrio onrroiib 
adjusted fio that tho rise in tcmiioralui'o was about, 
the name a before, Rft-vo n, HOOOIM! equation, HO 
that ft could bo eliminated and S determined. 

Tho torgmt ourrcnlfl <>C 8 through tlio apimvatiw 
were of IJin order of O-fi litrti ]icr fteconil. The ralo of 
flow was Icepli coiiBlnnt by nn aiilcmiii.tio pressuro 
regulator. It was i)irauvetl by pnasing tho giis 
through 1(1 iitu> metal Lubes arranged in parallel, 
niiil observing tlio pnsisiiro diflWcnce between thoir 
ciKlfl, Uio menu pre-fiaim:, mid Uio Innpm-atnre. Tim 
expression Rivinfi Uio riilo of flow in terms of theso 
qtumtitics was found by a wiries of ojqtorimcnla in 
wliieli tlio gaa was pumped into a reservoir of about; 
50 litres onpaoily, and llioii allowed to discharge 
through HID apparatus, Hy means of a special 
device, tho limes Inkcn for certain qnantitica of Ran 
lo pass through tho apparatus wero recorded auto- 
nmtically while tho gas wan notiially flowing, HO that 
tho initial fhictiuvtioiiFi ivcro avoided. 

Tlio value of tho clcotrio ourreiit was obtained by 
measuring tho potential difference set up at between 
tho ends of a, standard resistance c3l In lornm of 
cadmium colls. Tho heating oftoots uf tho Iradn of 
Uio healing coil wcro dotcriiiincd by oxperimontH 
mado under tho oxaut condition!! of tlio main experi- 
ments. 

Tho lino In tcnipcmtnro in the main experiments 
wan about 6" 0., anil it was measured to 0'001(J. 
Thufl tho apooiflo hea1 ii'oro meimurecl practically 
at Binglo temiiomliires instead of over lurgo ranges. 

TJio validity of aflminimR Uio licafc Ims for a given 
rifle in lomporalnro lo ba indopondciil. (if the rate of 
flow of tho gns wan tested by experiment. Tho 
matter was also oxmnincd from it thenrotioal Btand- 
point, and oorrcotioim worn calonliiteif mid applied 
ivliero tho OBflnmptioiiB made in tlio elementary 
theory ivcro snoh as lo lead to error* of moro tliaii 
about* ono part in 10,000. Tlio corrections wero 
snmll, only amounting to ono or two parlfl in 1000. 

Full dotallfl ol vftnoua other prconutiona arc 
given in tho original paper, and tlio moan ol a 
largo miinboi. 1 ol observations gnvo tlio follow- 
.illrf i 

Air 

21173 oal. per gram degree i> 20 0. 
100 0, 



0'20202 oal. per gram dogrco al 20 0. 
0-22121 ' 100 0. 

10 Bovoml dotorniinntiona- agrco in. oaoli 
to about 1-6 pailfl per 1000, and tlio mean 
It&iitrQ probably coruoot to ono part in 1000, 
iio' : values of tho specific heats obtainot 



ire greater hy about 2 per cent than 
irrcsponding values found by Regmiul *> 
by Inter investigators who have cm pi* *?*'*"* 
Methods similar in principle to that of -' 4<'* 
juanlt, but it lias now been established t' 1Jl ^ 
Llcgnault's method gives values which ni'O 1' J% * 
jy about this amount. 

(14) Si'Kcnao HEAT OP STEAM, 'Hi" 
worth 1 developed tho same method titV 
determination of tho specific heat of H^- 
at atmospheric pressure between 10<l- (*~ 
116 a 

i.) Outline of the Method. Steam is fjjo 
a ted in a boiler and thence led to ono liml > 
J-tubo pressure regulator. Tho prosmii-'* 
tlio steam forces tho mercury down in thin 1 i i > J l * 
f Iho U-tubo and up in tho other liin ~ 
which the adjustment of 
supply of gftH to tho largo 
burner, used for boating 
water in tho boiler, is 
After passing tho regulati * 
s leant, now inainlainiid 



llt 



I*" 




N Fro. 13, 

"II 

rfa, and rf 3l (lmliwforc.omlonae(l \v4itor. 



in 



ii 



constant pressure, IB led between tho 
tho jaokot surrounding tho calorimotor i>i.- 
thonco through a separator and a throttlo 
the spaoo enclosed hy the double-waited j 1 1 c t It ' I , 
whonco it passes down tho calorimotor llmv- 
tubo to a oondonsor, Dnring tlio pnw%Ko *-f 
tho steam tlirough tliollow-t-ubo ititt ]u;itt*#l 1 *v 
moans of an olcotrio ourronfc passing Uirtvi|j;li 
jilatiiium lioating coil, and its tempera tin-** 
measured on a platinum resistance thoi-fn 
motor. Another tomporatni'o moiianvonntiil 
made when tho supply of electrical onorjufx 
out off, and tho difference- between llui'Mti L\ 
tomporaturos gives tho rise in tomporiitiiv** * 
tho steam, 

(ii.) Galorimetna Arrangements (Fi(f, lit). 
Tho calorimeter proper consisted of a gl IVHH, t 1 1 
Y, about CO cm. long, in which thohoiUitijj? '* 
C and tho thermoinotor N wore llxotl. MMi 
tube was jacketed hy another glass UiVn;* 
which enclosed the length occupied 
lioating coil and thermometer. 

Tho calorimeter (low-tube and its 
ing glasa sheath were carried on a split 
cork wound with omega tapo and fixed, 
a ateam-tight joint,' into a space onoloBOcl 
doublo-wallcd brass jacket. Tlie lowot- 
1 Phil. Trans. A, 1015, ccxv. 383, 



lj|t t 



CJALOltBlKTJtY, KLUCT1UCAL METHODS UK 



of this jacket cowiminientra with a dcmblc- 
wallcd side tubo and tlio stonm entering at K 
passes between tho jacket walls to V, which 
comninnicatos with tho stonm separator U. 
It then enters tho inner portion of tho side 
tubo through tlio throttle T. Thin tnbu is 
tightly packed with gau/,o dines; tlioneo tho 
fitonm passes up tho tnlio S into tho top of tho 
flow-tube at I', and descending past tho heating 
coil C! and Iho thermometer N flows away into 
the condenser at ij. 

On its passage through tho tightly packed 
gauze discs in the side- heating tubo tho steam 
was heated up to the temperature- of tho jacket. 

In Fig. Ill, whiiili represents dii a grammatically tlio 
iimuigomenl thus desoribnd, it will bo noticed thai 
tho cylindrical space inside tlio double walla of tho 
main jiioltot m divided into two compartment*) by a 
diflo K. Thin disc of brass wns soldered to tho 
inner jacket tubo about G em. from the upper end. 
Its function in to prevent tlio steam in tlio tubo S 
from impinging on tho rubber cork closing tho upper 
end of tho tube, and thus being cooled. 

Any slight cooling duo to tho steam striking the 
lower split cork in of no importance, winco tlio steam 
would lai wanned again during i( passage up between 
tho How tuho and Iho Hummnditig jacket. Tho whole 
of the jacket, tlio separator, and tlio connecting 
tubes wore heavily lagged with felt. A novel feature 
of tho apparatus in tlio " spiral " method of mixing tho 
ntoam, in which UNO in inailo of A. number of circular 
dines punched to lit (ho thermometer tube and then 
out along a diameter, bent, and soldered together to 
form a continuous Hpini I 
round tho thermometer 
(BCO 1% 14). TliiH 
method of mixing i 
found to bo a great 
improvement on tho 
gnu xo method previ- 
ously employed. 

Tho usual equation 
for tho continuous 
How method is 




where EC is tho elec- 
trical energy sup- 
plied, S tho required 
specific heat if ex- 
pressed in joules per 
gram C., Q tlio rato 
of flow of tho steam, 
dO tho rise of tem- 
perature of: tho 
|,' K]< !_!_ stoam, and lulQ is a 

term representing the 

heat losa. If this loss is independent of tlio 
flow, then a linear relationship exists between 
tho values of EO/Qdtf and 1/Q. This is 
found not to ho strictly the ca-so, and another 
term depending on the flow is inserted 
in tho fundamental equation which thereby 

employment of three, rates of flow, ad- 



justing Ji in otieh ease so that d<) remains 
the sitme, ft and k can bo eliminated and S 
measured. 

Tho value obtained for tho specific heat WUH 
0485(> cal. per gram degree at 104-5 C'. and 7ftO 
mm. pressure; then, assuming ^ t 
a linear variation with tempera- 
tui'o as experimentally dctor- 
mitied, this coiTe.spmids to a 
value 04S78 at 100, Loth ex- 
pressed in terms of tho calorie 
at 2(T C. 

(iii.) KJfcet of Impurities in the 
Steam. Steam in tlio immediate 
neighbourhood of tlio saturation i\ \ 
point is liable to curry small particles 
of water in suspension, which can- 
not bo ovnponitecl completely by a 
moderate degree of aujiorhcRb if I 
any impurities, such as salt in 
solution, arc present. Since 1 nig. 
of water requires more than half 
a cnlorio to ovaporato it, and tlio 
heat required to raiao the tem- 
perature of I gram of uleam 10 U. 
is only f> calories, it in necessary 
that tho initial filcani whouhl not 
contain more than I in 100,000 of 
water if tlio speoilio heat is to lie 
found correct to 1 in 1000 over a 
range of 10 U. 

The ri.4o of tho boiling-point 
produced by a; {iram-moleouhfl of 
Halt per gram of water in approxi- 
mately 1000.B 0. The proportion 
of suspended water remaining n- 
evaporated at any degree of super- 
heat 0' will bo 1000.1-/0'. The 
quantity evaporated in heating 
tlio steam from 0' to 0" will bo 
1000^(0" -Q')!0'Q", Tliis will jro- 
llnco an apparent increase of 
tlio moan specific licat of the 
steam over Uio range 0" 0' equi- 
valent to lOOOLff/0'0", wboro L ];m. 1C. 
Is tlio Intent beat of evapora- 
tion. It was found that this extremely simple and 
convenient reduction formula titled tlio wsulla 
obtained over dift'croiit ranges of temperature with 
extraordinary precision, and vecon oiled iippnrenl 
iliHorepancica wliich bad previously been attributed 
to omits of observation. 



(15) DKTEUMINATION or TUB 
HEAT OF Am ANI> OTHKH GAHKS AT BOOM 

AND LOW TOU'ERATUHHS BY TUB CONTINU- 
OUS FLOW ErjUCTitioAij MKTiion. Hohcol ami 
House 1 3iavo determined tlio sjicoifio hnat ol 
air and other gases at +20", -7S,nnd 18;i 
by tlio continuous How inoLiiod. Tho air was. 
directed in a steady stream through n pipe in 
which it received a known tunount of heat by 
means oE a lioating coil. 

J'iff. Ifi shmva tho glass calorimeter in tho 
form in which School and Jienso used it. Tho 
1 ..IBB. A, Phiis., 11)13, xxxvll. 71). ' 



OALOItlMKTHY, 1'ILEOTIUCAL MKPHODft Off 



Q, 



HUH, wliinh in brought to a Htcady timi|ii!ratnro, 
onliTH llio nilnrimnli'i' from Inflow and flown 
through a .spiral, then through two ^]HHH jiuskots 
(! itml I!, nnd linally nauilios l.ln> ininu 1 tube A 
wlmih {lontniiiH tlio 
(soil, Tlio (omiioralun 1 ? 
tint in- and (wUlwviiig #i 
/j am dulorminoil liy tlm 



M 



J 



'A 



mid I'n. Tins wholo in Hiir- 
I'lHindiul liy n viiomini and 
a (,'liiHd jiir-kot mlvtii'dd inmcto 
ftinl is i!(iiitiiiii(!il in a liiifh 
lit M mutant toni]wi'atimi. 
AH Mm nil 1 ut lirht flown 
through lli jmslcHtt (! and 
I! Imfoni it rcimln-H tlm mil 
oalfii-iniolor, it ulworliH dim 
gri'ulor part of flio hoiil 
tfiwm oil' (.o MID in i ior viusuinti 
iKsinmlinjf to tint iiiinciplo (if 
tiwmtor (iiii'i'dtil. mill tliim 
(iBHisla ihn iiiHiilniinn (uition 
of HIM jiuiltol:, Thia firmilly 
iwlu<!{! tliii IOHH of ]HHL(., 
Imt <1nos nod ontlroly i>ni- 

vunt it, '.I'lm lnni|iomtim> of llio oiitll 

Kns in iiHwmmid in tlio tmiiHvo.i'HO Hinvl.Lon 
Tho lidiLtiiif? noil in B)IOWII in Fiy, 111 and 

nutiHinU uC iioiiHlanLiin wiro K and iw woniid in 

two HiHtllimm on 11 gliiHH )i)it, 



If 



ll'ltl, 1ft. 



iii f>nlcr l<> (li.tli'iliulo tlio licut ('(|iiiilly llm iv ' ' * 
uro liinind tdgidlicr and wound ruinx] thn linn ru| ' I '' 
Haii/n < Ij HH far tm HJIJITI! (icviuitii. '\'\ui wim miln J * 



ivory Htri|> M,,. 'I'l 



vii'c.-i wliinli condiml, Hui mil J ' 



*- % j 

"" '* 



' 






Icil ii|i through Ihn inner 
IHIVO Ki, with (ho ivinw ( 
MHiri'u of OKI (iiirn-nl. and to (lie voltmeter, 
lii'iiting (roil and a|i|iara(.nn f<u- mixing nni ciml 
in n In'iiBH pijMi j\l t wliiuli liln iiilo n Hcouncl 
[lijiii Mm "i[ a in ftmtuiu'il with Hi-alinj;-wax iir 
uninilar j^roovo 1111 till) iniiiu' ]iipo A, 

When working nb room doinpni'atnn! 
e.a.loi'ininidr was pliuuid in a lin-go wain- 
w] I Hfirroil. At low tomjioraturo, on (hn i 
hand, it was jilncod in a vacnuin vivmd v 
(iotittiitiod a niixtuni of ('(} 2 HIIOW and alin 
or lii[iiid oxygon, fn wioh UHO dim giiH, lu-f* ** *' 
(Ditiiring dim {inloi'iiiiDtwr, jinwuid through n jii J ** 
which was lionlnimid in tlui muno Initli an I I** 5 



" 1 



J * * " 



"'* 
'* 



Tho HH mo InveHti^al.!)!'!!, 1 wliint Hhitt.yi *)--' 
liolium and funmi other raro gustw lo low In** " 
lioraiiircH, nuidilifsil (.]i ajinaratim n n.-i ^ * 
employ a climoil isiraiiit. 

Tim ri'Hiilts thoy oM.airiod aro miminiirim '* ' 
in T.ahlo IX. T.liny also oalonlatiid out, I I** 1 
<!onu4])<mdiii(f vuluca for (lio idtsal $nn ulul*- 1 ' * 

1 Ann., 1. WWH., l!)l!i, xl. -17it. 
[X 



.,,,,, 


IV in Wai.!.- 
HIH-S, ]nn- Uriun 


1',. Iti drum 
('ill. tit IH" iHsr 
Urniu DI-HITO. 


(1,.. 


,, 


,w 




I.; 


,, 


1- JH 


fi."7H 


!.!! 


4-01W 






3-008 


MillO 


]-iii:-ii 


--JHO 


fi-aa 


1 !-(,, 


I-OIM 


2-010 


1 -iKM- 


2-1M1I 


l-(17il 


MlVlt 






I 


YUHOIIKN 












!- lit 


M-L'li 


:;-KI;I 


li (!(! 


-l-HVfi 


li'HIil) 


-l-87fi 


1-107 


1-107 


-- 71* 


1.1 -as 


H- Ifi7 


<i-:tiin 


-I-.-I7II 


(1','tlM 


'1-11711 


1 -15U 


l-'J/HJ 


-1H1 


1 1 '(IH 


^(l-l-l 


/5-;mi) 


:t-:i:iH 


fi-3211 


;!-;i^5 


1-51)7 


l-iiU.'i } 
| 








SlVlMKMiS 












-1- 'M 


1-0-14 


O'iMI), 


ll-OHil 


J-1181) 


II -1)111) 


4-1184 


1-10(1 


y 


- 1H1 


1-071 


0-i;fifi fl 


7-11IJ! 


1-8711 


(1-7 IH 


1-7M 


1-lllH 


1'llil I 






' 


OXVH1W 












-I- !!0 


((-Bl-t 


0-218, 


(J-UH, 


')() 


fl-7 


1-1)85 


1 :)() 


i-miH 


- 711 


(I-HI)H 


0-2U 


11-811 


<i -HI 


11-81 


-t-811 


1-UI1 


i in 


-im 


0-IWll 


o-sas 


7-30 


5-(M 


(1-1)0 


1-01 


1-1-17 


I'HH 
























Ant (i 




I W) a ) 










1- in 


1-1 H)H 


0-2-JOu 


(1-0115 


1-1172 


(1 -1)1)3 


4-IK1H 


1-101 


1-IIKI 


.... 70 


1-D1H 


0'2'IHp 


7-(M 


fi-Oii 


(1-011 


fi-IU 


1-101 


1-!H)U 


.-1HI 


1 -(Mil 


y.a-i fl 


7-2H 


.1-1)1. 


Q.8B 


4-8(1 


1-lfiO 


1 -H IM 




j-om 


Q^ m 


7-001! 


fi-01 1 


fl-Oftl 


5-Oflli 


1-308 


i-nnti 




I-OH-I 


(M'fiH, 


7-2'M 


I-1IS2 


(1-7.1 3 


*' m 


1-173 


1-117 



'jftlmilat(l viihiiw, k and k a (lie raLion fp/du and (-Vo/f-W ninnoo lively. 



CALOUIMETHY, ELECTHTOAL METHODS OF 



these results arc inserted for comparison along- 
side tho others. 

Tins values at constant voliimo aro obtained 
from tlio experimental numbers at constant 
rirossiH'o by means of l,ho expressions dedmind 
by a combination of 
tlic ordinary thermo- 
dynamioal equations 
ivitli .1). Jiorthelofc'fj 
equation of stale. 

(Hi) VARIATION OF 
Tiii'! .Si'iwiMU HEAT oi? 
Am WITH I'KHSNUKH 

OVI'lH TirM JiANUll 1 TO 
1200 ATMOfil'lIHIlKH, 

In 1914 Ho! born and 
Jacob l made a now 
series of measurements 
of tlui specific hoat of 
air high pressures by an 
electrical inothod, Tlio 
calorimeter employed is 
shown in li'iij. 17, Tho 
castings used in tins 
construction worn intido 
of nickel Hleul of high 
lonsilo strength. Tlio 
air enters tho calori- 
meter at tho bottom 
through asmall spherical 
piece c.^ and leaves at 
tho top through n similar 
arrangement <: s . Ho- 
twcon them) two points 
thoro is a nickel steel 
pipe fi s with Homieironlar. 
ends c a and c (|1 into 
which tho wido pipes c a 
and c 7 load for tho 
entrance and oxit of tho 
ouiTcnfc of air. Con- 
nections hotwoon tlio 
various pipes aro made 
by llaii^cH fitted with 



Ttui oil cn lio Iicntcd wlicn desii- 
mcaiiH of llm roHin(iiuco coil rj u , d in a Hfcntn 
fliu'roniuliiiff llic; ciddrimolcr mid (ho exit 
InnviriK tho cntraimn ]>i|io quid) free. '1'hin 
]H[iu w protoott'd iigniiml. liciit losn liy u WT 



-oil liy 

jiiuhot 

\H\W, 



A heating coil q l 
through which tho air 
flows is enclosed within 
the pipe r, 5 ; from hero 
tho air passed through 
tho annular spaces ^ and 
1%, ils direction being 
changed twice before it 
leaves tho calorimeter, 
The spaces /[ and. /,, 
avo oneloHod within thveo nieltol walls. Tho 
direction of tho air current is indicated by tho 
arrows in tho figure. 

Tho outor Hpauo of tlin (wlurimolni 1 in iilmi divided 
into two cylinder* o t and " 2 . (Imin^li whioh nil friim 
tho Hinall turbino r in driven in tlin dimition of llm 

1 Zeitsdir. Vereines Deiilxth. Ing., JOLJ, Ivlll. H2I), 




Q Dulfit* 



n[ (.wiiilod nilk and fruin t.hn aoiion of Llm in 
iiir by n gliiHH pijm iiiHcrlcil in it. Tho hwitiT '/i 
(ii)iiHiH(Ji of it gmii]) of (10 split niolfol tnbcs ttbnub 
-I nun. ionor iHinnrtor and] d-fi onlur diiiiimtpr, Tbt'o 
jirn fiictcnwl to two jinroclnlii jiliLlcH nnd urn licld 
tn^ciUn'j', tini! licliliid tlw olhi'i', liy olipti. 'I'lui nil' 
|mti.'u'ti Ilii-Dii^h nnd around Urn liilx'.i; (invn-nL in 
nnp|i!i(.'il to thiH liciiU'i' by M'ii'i'd intndiiti'd uilb (jhiHi) 



.18 CALOJUMKIMIY, METHODS .BASED ON THIS OHANUK O!' 1 STATJ 



Ill Hie liiuKi'iini Ilio black purl vi-jiroHciiU 

iiii-iru unll (ImHllHillid plll'td illlilllltlmg llllllt'l'illl. 

'.I'ho rrnnitn at a lompimilnro of f>!) 1 ' 
ro]irtWH*ntod by tho e-mpivioal formula 




whom 71 in Urn premium in atmdiqilwi'os. 

Tim valim 0'24i;{ obtained fur Mm H|iom(i<! 
hout at fill" and mm atimwplmm pi'CHHiiro 
a^niei vory mvtLHfantoi'ily wilh UIOHO obtained 
liy Kwim ('-ail a lit 20") nnd School and Jlmmo 
(SMO!)). .11. nf (!diii-Hi> dilVoi'H from liogiuuilL's 
valiH!, wliiisli in now known In ho low. 

Tim following tublo giviiH tho valuta oHivinod 
for tlm Jipmliu limit air n tomporatimi of f>i) (.', 
ami fin 1 viu'inim procures measured in kilo- 
gram por Kfj, oin. : 

X 



mol.rio Uioniminotoi'H 
dovfilopixl that tho 



blM'll mi hlK-' 



ntl 



no m-.i:' 



1', 


llolbiii'n utul Juliob. 


LllHrtJIllll, 


JiHilc anil 
'riniiiihuii, 


VfWl, 


Nocsll, 




(Olw.) ({'nit'.) 










11 


-^n;t 











E 


Wlfi -2-1 1 


270 








i!B 


-Mlffl -SI WI 


2711 


2-181 


2-180 


2-I03 


fit) 


2fiM 'i!5n 


HOI It 


2r>fi7 


2*1-1 3 


L'filifi 


100 


2(10(1 -2(11M 


:n>7f> 


2721 


2(llH 


2701 


1BO 


2B21 -aU) 


11118 


3)10 


2770 


2812 


auo 


2U25 -aittfi 




IllfiO 


28fi3 


mi 



, and tho lochniqno of 
if tlm jaekot Ima IIMOM gi'ojttl 
tated by tlio uso of elootrkml heating, 
the iiiliorout diflimillira iiHunomtotl 
mol'hod ,of (lalorimotry now ntuler cdiiHii 
Mini iiuiro than comilorbalamio the lulvnn) 
it ofTerw: iioiiHoqiioiitly, it in visry litflo 
at tho present day. 

'I'ho .ItmiHen iiio ealorimetcr and tlm 
stciini lialorimolur are olniwiisiil 
thin motbod of calorimotry. 

J)owar luia applied tho mimo 
to siiooilio boat determination a at 
low tonipeiufcurcH, and obtained dutu 
corning tho mean Hpooilio heat tif ma(< 
betwcon liquid liydrogcii 
liquid nitrogoii tomponituri 
(2) BlfNWUN'H 1(113 (1,\J 
MK'I'BR. Til tllJH 



i. 
fn*" il11 
tt>'* 

' "* 

h ->'" 



in <* 



])iiru<w(!n tho rofliiltH nf 
and tlui vuliioH oalitnhitdi! from tho 
oxiiuriinontH of .ionli: and '.rimniHon, 
(11)11), and Niiull (IHIH) Hit) liwwrtod. 
ivoro olitainod rroiu Lindo'H formula 



hoatgivonoiitby a 
ing from Homo higher tciu|H" 
turo to 0" (!, in (il)tiiim'il 
oliHorving tlio ooiitniol.inn u'li 
fciikoa pla(!0 in tlm (ilmngc f i 
i(!o to wa(:or produiidd |y 
boat given by tho hncly, 

Tho ohmtrviid voluino ulu" i 
iH eonvortod into culorirn 
vuhio for tho ooiiHlaiit uf 

ieo oaloi'i motor, i.e. tho JIHIHH nf rnoroiiry t\\n. 

into tho iiiHtrumonL liy tho additiim ii.f 

mean ualorio of beat. 
Numerous deLorminatioiiH of tliin mmsil.; 

havo boon mado and tho valuen uro Hiunntit r t 

in Tablo T. 

TAIILH I 



wlmro i Mm Hp<ntili(i lus/it iifc pi'PHHiirn (I and 
S Uin noolitig when tho ]ir(!i!nun' in roibmcd liy 
tbi'iittling from p to u vaniHliingly Hinall vulno. 



.lU r , JIIWIIODB 1JAHKI) ON 
Tlllfl OJIANOH OK H'l'A'.L'K 
(I) Tins Mu r nioi>."- ; ln thin claHH of oidoti- 
molriu anyllanocH tho ijuauLlty of liotit to Ifu 
moamu'wl IH dotonmiwd in tdrniH of any no 
of tlio following : (i.J '.Wio mnss of ion molted} 
(ii.) iitoain (jondoiiHtid i (ill.) liquid hydnigon 
or nxygon vnpoi'iHful. 

Rui'ili incnHiiromoiils do not rcqniro an 
fioourato inciiHiiroinonli of Binull tomnoratiiro 
oJuingos of tlm ouloriiiiotrio fliiiil, find taking 
111(0 odiiHidoi-atidii Mm Hlulo of thormomotry 
half it. iiciitiiry ago whwi MIIH nuithod waa 
inh-iHliHiiid, thin faitt wan iin(|iu^tidiiably of 
ixnil iidvnntngo. 1'iirfcliw, Mu* Uiniiinratiiri) of 
tlui Hurroitiiding atnioHjilioni (iiin havo but 
lltllu ofloot upon tlm indinatiotiH of MID 
fliilm'iiiHitor HJ mid tlui initial and final tompom- 
ni'O tho flivmo, tn rouont yourn (sidnri- 



Anllmrlty. 


Kin 






lllIllKI'll . 


IfHl 


1'hiL MOII., 1H71, 


Kll. 


iSi'linlicr and 1 
WuvMui . I 
Than 
Volk'ii . . 


1(5'R7 


Winl. Anu., IH7V, 

Winl.AHn'.* IHrtl, 
Ulull. (Miwrf. f-Vr 
1 1HU1. 


11. 

.vxi. 


Klnub . 
Dlnloi'kil . 


15 .2(1 
lfi-40 


( 181)0, 
Ann. Mttts., llHI.'i, 


St. V * , 


GrinHJiH(Hxor) 


Ifi-lt) 


\ lllli). xxvi. 1. 





might bo rumnrkcil (Jmi iniiiiy of (hi 1 
avo bused on uhsorvallimH of Ihi* 
lo tlio onhirhnotcr by a. mnnll <|ii 
of water cuntninnd in im mvohipci whom ll 
capiMJily wan omnpnrablo with that of llui 
water. iSinooin (lie majority ofcnwH im nlU'iiijn li. 
IJPOH mailo In vnry tho ooiulilioiiH find tluix I ' t *.- 
ByMlcinatiti orrors, all tlin vulurit avo not I'lititln^*! 
(Ito fianin weight. For exnmpli 1 , (ho HKHVU Miv*-n 1 
tlio menu of two ox(ii'imonU <""I^tt * 



OALOIUMETRY, METHODS BASED ON THB CHANGK Oil 1 STATE 49 



muter precisely similar conditions : 1,1 10 glass mvoloni; 
weighed 0-2 gin., cmitaincd (Kl gm. nf water, and a 
platinum sinker (weight O-fi gni.) wan also altaohed. 
Dictorioi varied tho quantity <>f wntor from 0-6 
gin. to a gm., and eunsecMioiilly liis delcrrmnnUtm 
is entitled to greater weight flian dm others. 
Griftiths 1 vnluc was obtained by supplying a known 
quantity of heal measured an clootrieal cnnrgy. Tlio 
heat mm mijiplied by a mniifjanin noil wound on a 
mien molt wliioh fitted tho interior tuhij of flio 
calorimeter (HOC Fig. 2), and tho rcmiKs are fwi.ied 
on tile olcotricnl units o[ KJ[.F. imd resistance. Tlio 
conditions wero varied. Tliun tho vatn of energy 
Biipply in the fas test experiments wns moro tliun 
seven times that in Iho slow eat, ami tho probable 
emir liy the method of leiiat s^unrea wan Iran than 
(H per oont. 

Bimson employed his ico calorimeter to 
determine tho latent of fusion of ico as follows : 

Known weights of water at a, known boiling 
temperature wore introduced into tlio inner 
tube of the oalorimotor and tlio contractions 
observed. 

In a separate experiment a known weight 
of ice at 0" C. waa contained in a bull), tlio 
rest of the space being filled with mercury. 
The ico was molted to water, tlio temperature 
being maintained at I',. M'oroiiry WHH drawn 
into tho bull) to occupy tlio sjmoo loft by tho 
ico in melting, and from the additional wnight 
of moroury tlio oimtmotion wa.s obtiiinod. 
Ho found that the malting of 1 gram of ico 
oauscd <i contraction of (HJ007 o.is. 

I'rom tlio results of tho two Hots of oxfiori- 
monta lie calculated tlio latent heat of water 
to bo 8()'()20 oalin'ioH, whiuli in 0-3 nor cent 
higher than tho value obtained in rawnt 
direct dotorminationt). 

Tho motlun] IH not a goixl one fordotort 1 "- 
ing tho latent heat of water, sinoo tlio oo'' 
tions depend on tlio diflovonco of tlio HJ 
volumoa of ico and water. 

(3) BUNHUN'S CALoiionwmi AHD 
MODIWOATIONS. (i.) Description, A 
ddaal tost-tulo A is fused into a Inrgoi 
bulb JJ, aa shown in J^jj/. 1. Tho bull 
furnished with a glasH Htoiu 0.1), whioh tc 
atesi in an iron collar 1). Tliiti stem ia 
with pure boiled moroury, which oi 
tho bulb to tho lovol /I Tho ronminc 
tho bulb above fi is Illlctl witb pure 
water. A calibrated narrow glasm t 
hirniahod with a millimetre scale, ia 
into a cork witli fine sealing-wax, and 
passed through tho mercuiy in tho ooll 
and made fast in the mouth of tho tub 
so that it becomes filled with mercury j 
by adjusting the eork in the mouth r 
tube QD tho extremity of tlio mercury c< 
in tho scab tube S can bo placed ni 
'convenient point, By methods, ivhiol 
described in moat text-books on pro 
physios, a mantle of ice ia formed arouii 
lower part ot tho tube A. 
VOL. I 



(ii.) Precautions in Vac. In tho original 
manner of performing tlie experiment the 
instrument, us doHoribed abnvo, wns plnccd 
in a vessel contnining pounded ioo or siimr, the 
top of tlin tulm A and tlie tulxi S alimo pntjuct- 
ing above tlie ice. Jt IH, however, genomlly 
found thut there is always small (JilVorontio 
in the fi-flo/ing-point of tlie iuo in the inalrii- 
merit and that of the ke outHidc. If tlie 
temperature of tho outside it to is higher, then 
thero will bo a slow molting of tho ico in the 
instruinont, which will oauso a iscmUimom 
creep of tlio nicrciiiry monistniH Itnviinls tlio 
instniineiit. If tho freezing-point of tbo 
ice outside ia lower tlian that of Hie ico in 
tho instrument, then tboro will bo a Blow 
frco/,ing of tlio water, causing tbo inenifinus 
to creep away from tho bulb. Tliis orcop 
generally ^_,_ h .,-.,. : ,_ T .. ,_,,,. JT s 
amounts to 

.') eontiinetrL'S [lor 



li or 

hour, nnd is. suflifjient to 
tnako it very clillicnlt 
to obtain trustworthy 
iiiensiiromentM. A slight 
ndditiun to tbo iimtru- 
nient will a Inn ml- rlinim- 
alo tbo (inieii, n.'diiising 
it to about a tenth ilo 
normal value. Thia ud- 
didion, Hiiggi'Hloil by Hoys, 
in pluditij,' (ho 
in Jin oinply 
vi'Hfael, tho top of wbiiih 
in (ilosod by a imrk thi'ougli 
wliiuh tlio tubi'H A and K 
|iaNH, This vi'Hwol i mir- 



1 




50 CALORIMETRY, METHODS BASEIJ ON THE CHANGE OF STATIC 



that the density of ico ia not n. constant 
quantity. 

Tho expori mental ovitlonoo on this point is 
briefly summarised below : 

Nichols l reviews fliti work of previous invesli- 
gatorji on Iho density of ico and iksodbwi life own 
experiments, Ho concludes that tho dotiftity of ico 
innntlcs, determined by weighing in petroleum, is 
O-niGlS + O-OOOOO, This result agrees with (ho mean 
valun deduced from different methods by Pliieker 
niul fjoinslei 1 , Ko|j]i and Bunscn (foi 1 a Bimihu 1 variety 
of iuo) to four ])!nec3 of (Icnirnals. 

His pspntimonta on tlio causes of thn variations 
in density of artificial ico wore not completed. Tlio 
method wns to freeze Iho i mantle around tho inner 
tube of a calorimeter by pouring in a mixture of CG a 
and other. Tho unfrozen water was slmken out na 




Jim. 2. 



oomplotoly as possible, and tho adhering water 
frozen, the remaining space- boing then completely 
filled with moKiury, Tho weight of tho moi'Oiiry, 
together with (lint of llio ieo, gave the data for tho 
compulation of the density of (ho ico mantle. 

Although llio results were consistent among them- 

KtAvca tho iilwolnlo value was siiliHcqnontly found to 

1 wins on account of thodeformalionof tlioglass 

"10 weight of tho contained mercury. 

""nifjlit tho (liHoro)ianey amount- 

"wcmi IIIH vnliio and Iliinson's 



waa duo to tho Jiiucn lower temperature at ivl*J* "^ * * ," 
mantle was formed ill his own cxporJmem.n. 
tlieroforo made Home (leterminatiotm willi nU 1 "' '' 
fnwon by means of alcohol at -5 to ~ 10" aa fff i 1 ^' 1 "' " 
ant in tho manner devised by HiniHon. '1'hn ni <-j Ml ' J '" 
nicnts nppemvd to indicate that the maiitl(n fa cr* 1 "' 5 ' 
by tho II.HO of alcohol at -fi" to 10 were li-u** el*' 1 '- 11 ' 
than those formeil by means of <,'Q a nml iil-l***'* ' 
-70 J by at leant 1 part in 1000, and further ill** 1 ' *' n< ' 
of the latter mantles decreased in density [ t y i M LJl1 - v 
this amount after standing -4 honr.i in an iim" fto- 1 ' '** 

Tlio use of C'O., and ether resulted in a vi.]-y v* l l*''' 
formation of ice, and tho mantle, when a eovl'nJ'* H '*' fl 
was reached, invariably became filled with n m^l- ^ v * " 
of (inn oraoks. 

Vincent* later took up the mibjcot, anil ul"** ^ M ' 
vestigftlod the coefiieiont of cubioul expatiHiou > *" i* 1 "' 1 

He prepared tlio ieo by means of iifree/ini' nii X *-' ' *'*' 
and appears to havo obtained a different cl*' llf '^'- v 
for each sample prepared. Table II. fiumtHnr' h5 *" ;t '"'" 
his rein]l( ; 

TALLE IT 



Experiment. 


Density Ico 
atO. 


Weight nsalpj 
the Ex lie rli 


u.Ml ' 

tH*Jtt- 


I 


-01 Q&IJi 


,1 


2 


0-91M60 


2 




3 


0-016180 


2 




Weighted me 


/"O'Olfcu'lO 
tO-OHiOUO 


1 

2 




n 0-OKiO 



His values for the oooOioiont of oxpansicni f (1-n- 
above samples are consistent, and no uoimt'tnl i< HI 
between variation in density and expansion I'JIM I" 1 
traced. Vincent's mean valuo for tho dcnui L.y i" 
I part in f>000 lens than tho mean of Iho ic.MiiLlri <>f 
Pliloker and Goissler, IJiiiiHeii and Nichols. 

Tlio experiments of Lcdno in IflQG Hiigj^"*'* 1 t<*n> 
caiiRO of the variations itt density which liml IM-I-.U 
observed by pro v ions workers, Ledun look *>x( r L mi' 
preoantlons to got rid of alt triiaea of dinK( tl v* <! 
air in (ho water used for manufacturing Lint l'n 
nain pics. Ho condonscd tho Btonm from l.x>ilii>}j 
wafer under oil (o obtain air-free water. 

Tho results of these cxperimontaiindiealiMl Hint 
tho density of ieo at wan not Icsa than O-IHV^. 
nnd as greater oJTovts wore made- to remove 1-i^ifi-n 
of gases tho values obtained for tho deiiHlt.y 1*1- 
creased. Ho concluded that tlio density i>f MJI-- 
free ico at would probably bo 0-0170. 

It in of interest to note that Ledno consUlaivi I lutt, 
ieo made from water which haa boon merely tn tllt-il, 
as in tho case of tho BniiHon calorimeter, tttill i 1 *!*!- 
tains about 1 o.om; of gasper litre at atmcmi;>lunrt-it 
pressure. 

Anotlior possiblo oaiise of tho variations in tloijMity 
is tho strains eofc up in Iho ico block on form IL -than 
and which disappear in the course of time. 

(4) JOLY'S STEAM CALORIMETER, (i. ) f/V/f- 
Method. In ths atoam calorimotoi 1 doviuotl 
Jo!y a in 1880 tlio lieat necessary to VOJHO 
tomporatura of a body from tho air tomportvtii r^ 
to 100 is measured liy dotGi-minlng tho 



| 



s. Me,, Ifl02, xv. 
B Proe. Roy. Soc., 1880, xll. 



CALORLMET.RY, METHODS BASED ON THE CHANGE OF STATE 01 



of steam which must bo condensed into water 
at 100 to supply this heat. 

The instrument, especially in ita -differential 
form, lias been found very useful for special 
purposes. But tho experience of moat users 
indicates that tho condensation method is 
more troublesome to use than tho method 
of mixtures for tho determination of tho 
specific heats of solids and liquids. In the 
hands of Joly, however, tho stoiun calorimeter 
has produced data of fundamental importance 
concerning tho specific heat of gasoa at constant 
volume. 

One disadvantage of tho condensation 
method is tho fact that less than 2 milligrams 



becomes at once filled with saturated vapour. 
Condensation immediately begins on tho sub- 
stance and the resulting water is caught in tho 
pan, weights being ridded to tho other pan of Hie 
balance so us to restore equilibrium. During 
tho process of weighing, the utenni is passed 
through very slowly (by opening mi escape 
tube loading from tho boiler) into the ciilori- 
motor, so as to avoid disturbance- of tho pan. 
After four or five minutes tlio substance 
has generally attained tho temperature of tho 
steam, and tho condensation is completed. 
The pan then ceases to ino'renso sensibly in 
weight, and tho equilibrium of tho bahnoo 
is maintained permanently. A very slow 




mo. s, 



of water is deposited per calorie, and conse- 
quently it necessitates accurate weighing. 

(ii.) The A2)paratua, Tho simplest form of 
Joly's apparatus consists essentially o a 
steam chamber of thin metal in which is 
suspended from tho arm of a balance a small 
platinum pan (Pig. 3), carrying tho substance 
under teat. 

Steam can bo turned on to this chamber, 
as indicated, and escapes through a pipe at tho 
base. 

It is essential to arrange tho inlet valve so 
that tho stoam can bo admitted rapidly for 
reasons which are explained later. 

(iii.) Mdlioil of Experiment, The substance 
is weighed with air in tho chamber and tho 
temperature- carefully noted. Steam in tho 
meantime is got up in tho boiler, and is 
suddenly admitted, HO that tho whole chamber 



increase of three or lour milligmmmcH pin- 
hour (duo to radiation.) in, hwvovor, notluwl. 
Lot 0j bo tho temperature of tho Hlcant and 
Ij its latent heat. IE JH tho imiraiHO of 
weight tho quantity of heat given out by tlio 
condensation is wL, and thin is expended in 
raising tlio Biibstmico and tho pan from <\ to 
ftj. It W be tho weight of Iho nn!>ntnnao, and 
s its specific heat, the boat acquired by tlio 
subatanco will bo Wa(fl, - (3,), and that 
acquired by tho mtppoHing pan will bo 
k(0 a ~ OJ, where k is tho thermal capacity of tlio 
pan, that Is, tho quantity of heat noccasary 
to raise its tempera-two 1" 0. Honoe wo havo 



The quantity fy is determined by 

observation, and tho tomnoralm-o ft,, in found 
either directly, by a, thormomulor inaorlod in 



52 CALORIMETRY, METHODS BASED ON THE CHANGE OF STATE 



the steam chamber, or by moans of liegnault's 
tables and a reading of the barometer. 

For extreme accuracy a small correction is still 
necessary. Tho weight W of the substance is found 
in nir at 0,, and the weight to is found when the 
substance and pan are in steam at a . The weight 
of strain per cubic centimcit.ro at 100 is littlo more 
than half that of air at urdiimry temperatures; for 
this reason tho weight to ia greater than tlio weight 
of vapour condensed by excess in weight of a volume 
t> of air at 0, over tho sumo volume of steam at 3 ', 
where u is tho volume of unbalance and pun together. 
Tho difference of weight of n, cnbio centimetre of nir 
at lii" C. and a cubic e<mlimoti-o of steam at 100 is 
00011116 gram, according to Kcgnaulfcj hence tho 
correction to ho applied to w in OOQIiJiOv. 

This correction being applied, tho weight of 
water condensed is determined, but it must be 
remembered that tho weighing is made in steam; 
and, if extreme accuracy bo desired, it is still 
necessary to multiply by tho factor 1-000580, 
in order to reduce tho weighing to vacuum. 
The actual weight in a vacuum of tho water 
condensed will therefore bo 

1.000B80(w-0-000030w), 
so that s is determined from the equation 



glolmles on the pan during the initial stages of tho 
experiment is somewhat counter balanced by radia- 
tion from tho steam to the substance. 



Reforonco should bo made to (0) of the 
article on "Latent Heat" for values of L. 

In order to avoid the condensation of afeain on the 
suspending wire, where it leaves the steam chamber, 
it passes, not through a small holo in the motal, but 
through a small hole pierced in a plug of planter of 
1'arin. Without tlio plaster the steam condenses on 
Hie metal and forma a drop nt tlio aperture through 
which tlio suspending wire passes, and destroys the 
freedom of motion of the wire and pro vents accurate 
weighing, With tlio plaster of Paris ping no snob 
drop collects, and tlio weighing can bo performed 
with accuracy. In liifl later experiment*, Professor 
July placed a small spiral of platinum wire around 
the suspending wire just nntsido the aperture, and 
by passing an electric current through Iho spiral, 
mifiioicnt heat is produced to prevent condensation 
on the suspending wire in tlio neighbourhood of the 
aperture, Hcsidos accuracy in weighing, a point 
of prime importance is the rapid introduction of tlio 
steam at the beginning of tlio experiment. When 
tlio steam first enters the calorimeter, partial con- 
densation occurs by radiation to the cold air and Iho 
walls of tlio chamber. So mo of the condensed 
globules may fall upon the substance- and lead to on 
error in the value of s. If the steam enters slowly 
this error may be large, and it is therefore important 
to fill the chamber at onco with steam. This 
necessitates a good supply of a team and a largo 
delivery tube, but when tlio chamber is well filled 
with steam a very gentle after/low suffices. If tlio 

... mijiply lio nut off, the weight of condensed 

lowly diminished. This arisen from the 

"T to tlio colder walls of the chamber, 

>m he again turned on (lie weight 

'-' of condensed 



(5) THE DnjTEmOTiAi, SUM-JAM CALOIII- 

METEH FOB THE DETERMINATION OF SrECIfc'K! 

HEATS or GASES AT CONSTANT VOLUME.- In 
the differential ' form of the steam calori- 
meter the correction for the weight of stcnm 
displaced by the pan IH eliminated. In this 
form (Fit}. '<!) two similar pans hung in tlio 
steam chamber, one suspended from ouch 
arm of tlio balance HO as to counterpoise each 
other. The thermal capacity of Iho puns 
can bo made equal, so that the term with k 
as a coefficient docs not appear in tho equation, 
and the radiation error will alao disappear, 
aa i.t will cause equal condensation on the 
two pans. 

Tlio chief use of the differential form is, 
however, its application to tho ealorimetry of 
gases. -Fur this purpose tho pans are roplaecd 
by two spherical shells of copper, ono contain- 
ing tho gas at a known temperature and tho 
other empty. Tho spheres are furnished with 
small pans, or " eatoh-watoru," to collcet the 
water resulting from condensation. Greater 
condensation occurs on the sphere which 
contains tho gas, and tho excess gives tho 
quantity of heat required to heat tho contained 
mass of gas from 0, to E . This determines 
tho specific heat of tho gns at constant volume. 
Tho great advantage of tho differential calori- 
meter, is that any source of error common 
to tho two spheres is eliminated, and the 
gas or other unbalance enclosed in ono 
of them merely bears ita own sham of orror 
and not that also of tho containing sphere. 
Thus tho effect is practically the samo as if 
tho gas woro contained in a vessel of zero 
thermal capacity in the single steam calori- 
meter form. 

Tlio spheres employed by Professor July 
woro of copper and about (H em. in diameter, 
tho ono containing tho gas being mtido to 
stand ft safe working pressure of about !lf> or 
40 atmospheres. If at the beginning of the 
experiment this space is filled with air at about 
22 atmospheres at 0, tho pressure will rise 
to about 30 atmospheres at & . In ono ex- 
periment 3 tho weight of air contained wan 
'i'28f)4- grams. The condensation observed as 
duo to tho air was 0'1(5217 grains. This 
required a correction to compensate for the 
difference in weight of the spheres. Tho 
corrected value was 0-11029, tho range f 
temperature, S -0 L , being 8<l.'52 0. In a 
series of six experiments tho moan precipita- 
tion per degree centigrade- was 0-018004. 
Tho following corrections are also necessary : 
(a) Correction for tho thermal expansion 
of tho vessel, and tho consequent work done 

J. .Toly, Proe. lion. Soe., 1880, xlvll, 21S. 
! Phil. Trans. A, 1801, elxxxli. OS. 



CALOaiMETRY, METHODS BASED ON THE CHANGE 01? STATE fi3 



by tlio gas in expanding to this inercnsud 
volumo, 

(ft) Correction for tho dilatation of tlio 
Bphoro under tho increased prossiiro of the 
gas us tho toiiipomtiiro rises. 

(c) Correction for tho tlionnnl effect of 
stretching of tho material of tho Bphoro. 
(Wires arc generally ooolcd by midden exten- 
sion, but tho cooling of tho copper in thin case 
is too small to merit consideration.) 

(d) Correction for displacement or buoyancy 
arising from the increased volume- of the 



0-1721. .L''or carbon dioxide, tho tsluwgo with 
pro.smti'o is shown by the following table : 

TAUJ.I: IK 



Pressure In 
AtmiwiiliorcN. 


'Density. 


<V 


7-20 


O-OllfiHO 


0-1118-1.1 


12-2i> 


o-oiwmo 


0-170.11 


10-87 


o-o as.) lift 


O-171-l-l 


20-00 


0' 03(5520 


o i7.m r 


2l'(i<i 


0-037802 


O-rmi) 




sphere, both in tlio air at 1 and in the steam 
at fl a , 

(c) Correction for unequal thermal capacities 
of tlio spheres, 

(/) Reduction f tho weight of tlio precipita- 
tion to vacuum. 

Professor July's cxporimonta uhow that in 
tho case of nir and carbonic acid tho sp-ooiflo 
heat increases with tho density, but with 
hydrogen tho opposite seems to bo the onse, 

.For air tho specific heat at constant volumo 
at a moan pressure of 10-01 atmospheres, and 
a mean density of 0'020. f i, was found to bo 



Tho moim result of tlio ux|>orimonl8 on 
hydrogen gives a HpoeHlti hunt JM02. 

((1) ].)K\VAK'S Liyirnt Ant AND HYJUHHIUN 
GAr,oiUMKTKji. Dowur l IIHH d^viuod a (idling- 
motor based on an aiuilogmia jiL-iiuiijilo to tho 
steam calori motor in whioli ho umploys 0110 nf 
tho liquefied gascd ns caloiiinotric Biibatdiico. 
Whilst Joly'a calorituotor doptinda upon con- 
densation on a eiild object, DOWIU-'B oalorl- 
motor dononcla nn the evaporation ns a immns 
of absorbing lioat from tlio hot objuut. 

'' JW ' it(K ' A> Ixxvl ' 3 " fi ' K v ' 



, METHODS BASED ON THE OHANCilO OF STATl'J 



of weighing tluuinnntity of gs ovnpo rated, ho 
determines llio volumo of gas given off from 
tho liquid whiuh, of cmirao, is at its hoiling- 
point. Now tho choice of Ikiuofied gas to IJB 
employed as calorimeter substance is ilotsr- 
mined nminly by two considerations : 

(a) Tho qni5iitif,y <>* & f? [v()T1 off by 
evaporation on tho absorption of one imlono 
of heat, and 

(ft) r J'ho range of tempo mtu re availul>lo 
throiigli whioli substance is cooled. 

Tho table below summarises tlio data lor 
so mo of tlio possible gnses : 

TA.BLB IV 







I.liinld Volume 




Viilumo fit Una nt 










(}" mid ('liO nun. 




(lljlllt. 


IKilllDg-poim 

iTHJ.t. 




Jioiiu ""'., 


Sulphurous acid 
Oarboni{! ncid - 


I-10-0 
-78'0 


0-7 

0-llJi (solid) 


97-0 
142-4 


a-o 
a-o 


Ethylcao . 
Oxygen 

Nitrogen . 
Hydrogen , 


-103-0 
-182-5 


1-7 .. 

0-0 
1-3 
11-3 ., 


110-0 
6S-0 
fiO-0 
120-0 


7-0 
13-2 

Ifi'tt 

88-0 



fi() u.o. capuwty, 

a long narrow tulni U, projecting aliuv*' 
month of A, mid hold in its plftu l>y H1 
loosely packed cotton-wool. From tho 
of thin narrow tube, either beforo i' 
passing out of A, a hrani'.li tuho M Js (.ulti'ii 
ti cimblo tho volatilised KIIH fnm) llm '"! 
motor to be collated in tlio mtnivur I 1 '. 
\viitar, oil, or other Hiiitablo liquid. '1' 
extremity of tho projecting tulm (! M1 
tost- tube 0, to contuin tlio portioiiH of ma*( 
oxporimenled on, is attached by a (tin* 1 * 
flexible rubber- tubing J), tlum Eo 
movablo joint, whicli 
bent HO an In tilt n '" 
tho small phiOOH of HiibHl,f 
uontainod in (J into ilio 'i. 
motor, ami \vliioh iifl 
assumes n juiititiuti 
Homowliat lilto that 
diagram. 

With cavii it in ]>Hnllil 

iv mn^lo pii'iHi at a linm f 

iiitit II, lint nil ini]>rnvi'it 

of thin I'l'doidiwli) in olic 

In it., I 



of 
in 



to 



It will bo observed tliat oxygen givca off 
13-2 o.c. poi- caloric wliilst otliyleno gives 
only 7. Hydrogen gives off 88>0 o-o. tmd is 
particularly advantageous but for the (not 
that tho manipulation ia diffloult. Although 
nitrogen is ft littlo bettor than oxygon, it is 
preferable* to use tho luttor for tho following 
reason. The boiling-point of air is liolow tliat 
o oxygen. Even if thoi'c is no tayor of cold 




oxygon or gaa on tlio aiirfnco of the liquid 
oxygon, tho air coining in contact with it 
through tho ncolc of tho calorimeter would 
still remain gaseous; but if liquid nitrogen. 
is need tia (lalorimotrio substance, air, being 
heavier than nitrogen but having a higher 
boiling-point, would, in falling down tho nook 
of tho calorimeter, come in contact with tho 
cold gaseous nitrogen ftnd bo condensed, 

(7) TIIK LIQUID OXYGEN CULOiiiMiiTEn. 
It consists essentially of a htrgo vacuum 
vessel A (Ftg. C) capable of holding two or 
throo litres, into which is inserted the culorl- 
motoi 1 , a smaller vacuum vcsaol U of 2fi to 



tyj,, In it, I 1 in a wir 
through tho eorlt (J, HtUnl into (ho jiioiilli 
Icst'tubo l.'[, ullnohed by u lii'iiuoh thi'oiiuli thn 
riibbtir luljii J>i to llm und of <!, na lu-fon-. 
Uii! oud of tlio vim ]' in it lumlt, by whliili un | 
of tlio liiibHlamio. fit a tiinii Dim In; jiulli'd nf 
dropjied info Jl. Whim no other 
made, tlio pi>rlioiin of iniillor 
at llm lcm|iorftliiro of (ho room ; but ivlu-u I 
tempera In ren ftro reiniii'iid inilinlly, n viimiiiin. \ 
U, nontniniiiK oithor nolitl earlwiniti ucM. l.i 
otliylouo, air, or otluir !>, oan bit pinned m> n 
envelop tho tcrtt-liibo <! or (!, j or if hiHb<T l<'ii| 
tnrc.'i nr-o roipiircd, tlm ftiirrouinliriK vcNsii'l niu 
filled wllli tho vapimr of wtildi 1 or nlhri' lEijiiUi". 
Now, when a (jiiimtity of liquid iair linn lici'ii in 
(oinf! volalilinivtii)ii for it (tine, an llio nilvngcH nvi 
ntim movo ((iiintdy than tint osygon lint liuilinjj;- 
MUDS Hlightly. Two jiointH rciniirn 
uf lliin ; lii'rtt, tho 

of (]w liijidd air 
ono JHtrlrs of oxpm'imfiiilft j no.xt, tlio ]-i-vi'iil U 
n. teiidonoy for tho oaloi'iinotw H to "mink In 
Bomo of tho already voltitilimid KIIH. Jli i nrO 
oxterior vessol A nlioiild bo filh-d witli n, 
(pmntity--Hi)mo two Hires of W llijiild itii-, 
tainiiif; n higli pnrociitn}(o of oxygen, mid lliiv ii 
motor ilflclf diioiiUl l)o filled with ttomo o[ llm 
fluid. Thin will iniiinttiin vory nlosisly llm inni 
tomporatuvo rcquirnil. When any "imnldiiK In 
Hoonia to bo laltiii(( pliioo, tlm cnlnrlmnlcp nlnm 
omplicd and fillnil unvw from tho lururr iln* 
Tho Uibo botweon tho oalorimotor and tlio n'i r*-i 
fihould bo of llio mo of wido quill In bin jr. nil 
lower end uliovild bo BO lUTAiiged blitw llm m 
of tlm liquid in llio collecting \mw\ nn It) |^i< 
roHHlUnt prcSHui'o. With miuli preoauHoim, 
limy easily bo obtained correct In within 3 |ii*r. 

Tho instrument having boon Hot up imc.l 
with liquid air, an oxportmoiib is cmiuli 
by tilting up tho littlo toiit-tiibi), 



CALORIMETRY, METHODS BASED ON THIS CHANGE 01?' STATE 55 



cooled or heated, thereby dropping into the 
calorimeter a portion of nny substance previ- 
ously weighed. Tho substanco in this way 
falls from tlio temperature of the room to 
that of liquid air. The heat given up by it 
volatilises somo of the liquid, which is curried 
off by tho brunoli tubo and measured in tho 
graduated receiver ]?. Immediately preceding 
or following this observation, a similar 
experiment is made with a small portion of 
a selected standard substance, usually lead. 
The quantity of lead in so chosen us to produce 
about tho same volume (if gna in tho receiver 
HS tlmt supplied by tho portion of substance 
experimented on, ]}y this means tho circum- 
stances of tho two observations are made aa 
similar aH possible, and thereby many sources 
of error arc eliminated. 

(8) LIQUID HYDROGEN CALORIMETER. 
In 1913 Do war * further developed the 
method BO aa to adapt it to tho range of 
temperature between tho boiling-points of 
liquid nitrogen and hydrogen: from -190 to 
- 2513 C., a ran go of only 57. 

Tho liquid hydrogen calorimeter ia a glass 
cylindrical bulb vacuum vessel A (Fig. (t) of 
fiO o.o. capacity, silvered, with -J- cm, slit. On 
tho nook ia sonlod a glass tubo B. This 
projects through tho brass coned fitting cap 
If of ivn ordinary slit silvered vaeumn vetisol 
in which it is supported, A side delivery 
tube, provided with stopcock I), is scaled 
nofir tho top of B. A short length of rubber 
tubing on the neck of Iff makes a gas-tight 
joint with B. To minimiso splashing, and to 
reduce tlio impact of tho falling pieces, a thin 
strip of German silver or lead K, bent out 
neat the top into a shoulder about 1 cm. 
square, stands centrally in the calorimeter A. 
Tho strip is out from a thin tubo of about tho 
same diameter as tho calorimeter neck. A 
short length of tho tubo is loft above tho 
shoulder, and supports tho strip by fitting 
loosely into tho nook of A. Somo such 
dovico ia essential in tho uso of this form of 
tho liquid hydrogen calorimeter. 

Tho calorimeter in its turn is immersed in 
liquid hydrogon in tho supporting vaomim 
vessel C, tho nook of tho calorimeter being 
8 to 10 cm. below the liquid hydrogen surface, 
Tho vacuum vessel is only slightly wider 
than tho lower parb of A, and is provided 
with a eoncd cap V, whereby it is also 
supported and completely immersed in n 
wider vacuum vessel Gf containing liquid air. 
G is also fitted with a brass coned cover, 
fitting vacuum-tight on to tho cap F on 0, 
Both caps are pierced by two thin tubes, one 
for fitting on to the filling syphons, the other, 
bent at right angles, serving for connecting to 
tho exhaust in tlio case- of tho liquid air vessel, 
n.nd in tho case of tho liquid hydrogen to tho 
1 Prac. Eon. Soo. t 11)13, Ixxxix. 158. 



stopcock leading tho evaporating hydrogen 
through tho upper part of tho apparatus. 

This arrangement Lima charged only needs a little 
liquid nil' euoliod in every ono inul a Imlf hour. Tlio 
liquid hydrogen vessel will not need ronUmi wiling foriiL 
least four hours. Tlio level of (lie liquid hydrogen in 
tlui calorimeter (loos nut full 1 om, in MX houivt willi 
constant uso. The bulk of tlio materials added roughly 
compensates for tho volume of 
tlio- liquid hydrogen evaporated, 
His important (hat thin l*vol 
should not materially dumgo, 
since, of tor striking I. hi; shoulder, 
bodies move more slowly, ara 
deflected on to the cold wall, 
and low results 
lire obtained duo 
to tlio longer 
cooling of the 
nmterials in the 
vapour lii'toro 
being inimenml 
in ,Lho liquid 
liyth'ogon. 




Via. 0, 

Tho isolation of tho calimmelcr was nneli (ho.t 1ms 
than 10 o.o. of hydrogen gnu WUB ovtiporalcil from it 
por miimto, The wliolo n])|iaraliiH. w Bujipotlod 1)fi- 
twcon tho cork-lined spring jnwB monntwl on a heavy 
metal bnsc on wliioh the milor vnoiiuin vessel rest*. 

Tho cooling vessel H is eonnootocl by an 
india-rubber tube to tho top of tho calorimeter, 
It consists of nn ordinary oylindriaal silvered 
vacuum vessel, 20 om. long find 7 oin. wide, 
with a central axial opon tubo 1C mmliwl in 
below. . This tube passes throngh the liquid 



lift 



(JAUmiMETRY, METHODS BASED ON THE CHANGE OF STATE 



in tho viuiuiiin VOHHO!. It has bho same 
diainott)]' bolow us tho iik tube of tho cidori- 
muter. 'Ni'iu* tin! tup i>f the central tube a 
Hi i In tubu J, of about Iho name diameter and 
Hoimi II (MIL lung, servos fur tho introduction 
of tho woij.<hod piuct'H of material, which arc 
nil iiotiltuJ proviuiinly to Iho lorn \i am tu ro of 
liijuid ail', and tlum fall on to a thin metal 
(tine I* Jilting loowily tlio tnbo K, where they 
roiimin ahimt Ifi minutes. J, 1 in mipportcd by 
lining hitij^d lo two thin nbonilo rods, L and 
iM, llxod tn a briiHH Fitting comoiitert on to 
Urn tup. Tho r<id J'j is not fixed direotly to 
Mm diHii IniL Li i iv motal ring It. From tlio 
riiiH -it two thin vortical stool wires are 
isimiiouUsd freely In two jioiiilH 4111 Iho isircuni" 
f tlm pun hwlow. Tina rod and tho 
ritif* t;iin bn given a vortical motion 
by n oninh N in th fop Jilting, thereby 
tipping tlio ]iiin and i'<ih*aiiij fchn picuo of 
luatiiriril, w-luiih Uicn fullH frcoly down into 
thiHiiiliiriniHlc*!', Ahi^li viusmimJs niainlnincd 
liy a (H'oHn-tutM) S, opL'tiiuf; Id tlio anmiinv 
ii|iu<Hs llllod wiili tiliai'oniil. 

Ad lliu linnjii'inliiro of linillti^ nitmycn, tlio 0011- 
vnHlliHi inivronlM hi U)i! vcittrnl tnlio of siieh iv vcsnol, 
wlii-n tuniiKMjlcd Ui Hit' Kiiltinnidlci 1 lnvlinv, Imvo no 
.Hiivloim ufl'tnt oil tin* toinpnmtiiro in this tubo nt n 
ri'iimumbla Uiiilanuu from tho liottinn, pravidcil Uio 
m-tilnil luhd ho n<iL wiiii- 1 . With a InrRor piillcni vrasol 
tlu'widUntf tliin uciil nil till 10 WUH im)it>nncil t2-2om., 
tn Hi fivni IHJW Uin iliifcrt'iico won unilur i) aL (ho level 
of Itm pini. 'J'Jicao tcinperiiUirt'tt wcro mcnmircd by 
n niimll livllnm llii'riiuinitiii'v, consiHUng of a d-o.o. 
Inilli Ui wliiish wiitt WNibsil a Hiuall moron ry iniuunnclcr 
of Iliui i-ii|)illary lulling. 

'J'li hydi'iiK''" cviUMn-'fttiiiK '''<>'" ""> Htjiiid in Iho 
viiiiuiiin vcHsiil (*,in wbioli llioi'iibminelttr i iinmorflcd, 
IM ctniiloyi'il In UifrintiTvol cif ubHprvn lions to rnnin- 
Inin n hyili'iigi'ii ntiu(is|i!L(-ni llu'ongli tlio ncok of this 
cnl^riniDti-r innl tlm (MHini-dti'd iiifiimirinK lubeH 
IHnlt of Holid nil- in llii- iNilnnmnlcir nwilt iw HIUH olivi 
ulril, A nini|itis iirnin^oiiu'iit <>! it I lir(!i!-wny uoolinjj 



of a jduHM tnljc 8 oin. 

in iliiunotnr and 'If) ons. long, open at the 
bnLlimi and pmviduil with it wiflo T-pieoo at 
th(! Lop. Tho lubo in iinnnTHod to tho nnok 
In wiitm- in a glum oylindnr, and in omuiler- 
l by n, wmjrlil im<l curd running over a 
/ jiiht abnvci. 11. in thiM-ohy readily 
I dm'intf tlio limu RUN in being wapnratei 
Dui (Milnriniulpr j Ibis ensures that IK 
nriwHiirn to iuxidncHsi'1. Ono arm of the 
in ciiwii mid oonncctlfl to the ntiioiiuk 
.D'on Urn cmliirimcitor nooli i (bo nllier in 
provided with anotlmr aniftll stopciock mid 
(')innwlH 1't a SIHt-n.n. gafi bui'otio \V similnrly 
iimiwiwd in water, Thih latter sloneook i 
ohiHi'd while Ihn M IIH ovii[)i>rated during an 
oxpui'iinwit IH titilk'filod, 

TboHO tirrBiiBommifi nre noccaflnry to HCOIIVO tbo 
Niinininm Impediment Ui the ovniioniting liyilrogon 
whioh \* iiBiinlly ovotvcd in ICHB than 10 Ht-condB, anj 



fniiii 
haul; 



cnipm'Jiry bnok pressure being fiilnl to ( i ncoi'<l^ 1 '* 
L'fiiilts. At leant 16 seoouds arc allowed tor noil*" 1 " 
rig tho gas given oil, and even longer, in s.omo on **' ' ; ' ' 
ivith budly conducting bodies, 

AH far us iKiNsible tho materials imod woro t"" %H ' 
n this forms of aplieros ahnut 8 mm. diuim^*' 1 ' 

In tlio cnso of liquid bodies, the irmuM ^V H 
'irst coolod by liquid air. liYcriiionll 
wore fiw.uii into acilid cylinders in thin 
iitljing, and pieces cut off after removing t-' 1 *' 
flaas mould, Tho mctallio vnatorialH HV** 1 "*' 1 
u Homo cases fused into buttons of donvon J* 1 ' 1 
rt'oight in an oxhauated qnurtai tnlio, * ' ' ' lt ' 
ead, howovor, of whih many piccow \v <' 
1-cq.uii'cil, was cut from rod, and smbHcquoK 
Hqucc'/.od in a small sjihorical mould. 

Volatild binliea wore weighed at ib l 
tomrjoraturo on a lif'lit Gorman mlvw 
Hitpportiid by a thin platinum wire HU ] >u ti t* * " 
'ruin tlio balance pan about 2 <im. nbi)V*i t. 
,ovol of liquid air contained in a wido (ti' 
vaoiium vosHol. Koine materials would ii 
malto (lohoront hullots or cant stickn, anil tli"' 
wore filled into very thin-walled uylim 1 1 1 ** ' 
motal oapHiileH. 

In order to obtain oonsistont n.iHiiH l- 
noeesHary to employ oxaotly the HUIIIO ;pi 
ooduro in oaoh teat, but with this uppuiNtt- 
Ilownr waH al)lo to obtain results whioli rn r 
varied among themselves by nioni tlum -- 
'A per cent, 

Tho tlntu thus obtained for tho IIKNUI HiH'^ 
beats of fi3 elements at about fiO^nlm. t 
aninmarisecl in Table V. 

TABLH V 



*J 





Atnlilla 
Wultflil. 


HnocKIn 
D-0212 

ii-init) 
0-07 ia 

0-037J 

I). 077.1 

0-OJtll 
0-Oli-W 
0-OIIU7 
0-1 S 
0-07U 

0-ositr. 

0-OM2 
0-0230 

o.onfi 

0-020S 
0-01107 
0-024/1 
0-ffllfi'l 

0-02fiB 
0-03(11 


A I - 

J -Jlfi 

It- i :J!Jli 

0- Hi 

u-f t:i 
a -Tilt 

l-V-l 

1 - 1 :H 
HU 

ii - -j i 
i. -vr. 
n-ni 
o HII 

] -rin 




7.():t 

0-1 

11-1) 
13-0 

SIM) 

27-1 
SB "I 
28"! 
31-0 
31-0 

UIHfi 
40-1 

48-1 

BS 
56-1) 
(58 -7 
50-0 

(15 -4 
75.0 
71) -2 






< 'nrlion (Ali(M(in gra|)hilc) 
Diannmd 


Maflncmum .... 
Abuuiiiiuiii 
Silicon, (iiHGil, clc-o. cnio, 
oryHtiillincil - 
I'hospliunm (yellow) . . 
(rod) . . 




Calmnm 
'ritniitinn 
( hromhim - 
MflnRuncHO 




(,'obalb 











CALORTMETRY, METHOD 01? MCXTUIIES 



TAHLH Vcontinticd 



Kleiueiit. 


Altiiiilt: 
WitlKlU. 


SLicdflt! 

Hl'Ht, 


Atiimio 
KuiU. 


Ili'omims 
lluhidium .... 
Ktronlimi), iinpnro . 
Xiroiimiim , . ... 
Molybdenum .... 
KiiUiouiuni .... 


7IM)(i 
H5-1 
H7-H 
00-H 
OlH) 
101-7 


(t-O-fliS 
0-07J1 
O-OfifiO 

o-02tt2 

0-0111 
0-0100 


!M13 
(1-Ofi 
4-82 

2-na 

1-30 
Ml 


Piillrulium .... 


10(1 -ft 


0-011)0 


a -03 










Tin 








Antimony .... 


mo-2 

] 211-07 


( MIS-JO 


2-811 


Tollurhim 
(Jni'sium 
Harinm, impure . 
Lanthanum .... 


127-0 
132-ft 
1374 
138-0 


0-0388 
0-()i513 
0' 01150 
0-0322 


8 -(18 

0-82 
4-80 
H>0 


" Biilymiiim "... 


142 


0-032(5 


4 -(13 


























(JnUI 


















201-1 








207 




'(IK) 


Ilitimiii.li 
TJiimum 


!!OH 
332 -ft 


0-0218 
0-0107 


l-'M 
4-fi8 











Tlui in toi'tiNting faot d hoovered in tins 
course of this investigation was tliat Uio utomio 
lionts wore periodic funti Lions of th atomic 
woight, ami tlio curve roaombled, gonorally, 
the well-known Mayor atoiniu volume for the 
solid state. 10. o, 

OALOUIMETBY, METHOD OF MIXTURES 

(1) INTRODUCTION. Galorimotrio appanvtun 
assumes the most diverse form, oaoh typo char- 
acterised by certain features, which adapts it 
especially fur a particular el aw of iiioimui'omtinlj, 

J.i"oi' tlio ilotormiiuition (if tlio moan Ftpodfio 
lioat ot a HiiUatuneo ovor a mii^o of loiiipcmtnro 
or for lh (kitoniiimilion nf thn himt of oom- 
biiflUon of 11 funl tlio Motliod of Mixtures 
ifl a ijonvdiiiont uno to employ and SH probably 
tho bout Itntnvn of all oaloninotrio mothodH. 

(2) THI-J Mi'M'inn) en-' MIXTWIIKS. 'J'ha jirin- 
ciplo of tliin niothod En to impart bhti quantil;y 
of hont to lio inoiwiirod to a known mnss tit 
water oontaincd in a voHHtil ot known tlionnal 
oapnoity, and to obmirvo Llio rm\ of tompm'a- 
tui'o produced ; from wlimli djitu, an oxplained 
in detail farther on, tho (piaiitUy of Imnt uu 
bo oalmilalod, 1'hto molbod in tlio tuniploHt nf 
oalorimotrio mothoilH, but in not Urn inottt 
aoonrato. ]foat in loot in truiiufcrnng dho liot 
object to thp caloriniotor, and although id cull 
bo mini mined by arranging Uial tlui transfer 



tnkos pbuic mjridly, it unnnot bo cliini-inttcd or 
even ftooiii'dtnly ullowad for. Soino lieat is 
loat when tho onlonmolor is raised tihovo tho 
tomporatiiro of ita oiioloauro niul bofore tho 
final tonipwaturo is rcuched. This can bo 
roughly estimated by olmorving the raio of 
change of toiiiporatiivo niui aKBiuniiifi that tlto 
boat loss i directly proportional to tho 
duration of experiment and to the avcmgo 
excess of tcmporaturo. Tho accurate deter- 
mination of this correction in of fundamental 
importance- in this method and n del ailed 
dinmiKsio'n of it will ho given. It in always 
desirable to diminish the lona of lumt as mneh 
as possible by poliHbing tho oxtorior ol thn 
tialontnotor to diminiah radiation, nnd by SIIB- 
poiulinj.; it by non -conducting HiipporLa insido 
a polished case to jiroteet it from draughts. 
It is also very important to keep tho surround" 
ing oonditiuns as constant ns possible through- 
out tlio experiment, Thin may bo scunrcil by 
lining a largo \vatci]'-bii.tli around the apiifiratus, 
but in isxpcrimoiilN of long duration it iw 
adviaablo l.o utiis an ninsuralo toinporaturc 
i-egithitor. The melliod of lagfuing tho (uilori- 
motor with co|,toii-\vonl, wlmiii in often re- 
commended, (limhiiHlu'M tho heat IOHH 1^011- 
Biderahly but rendcm it vei-y uimc-i'tohi, and 
should never Im lined hi work of precision, si mso 
tho had condnetoi's tuko HO long (n u-aeli n- 
stemly Blate that tlio rulo of loss tl(ij>oiidn on 
tho punt hintoi'y more limn on tho (< v iii]ioralurw 
of tho calorimeter at tlui monicnU A moro 
Horion.H oljjoetion to tho UHO of la^gin^ of tlii 
kind i thu dangur of its absorbing inoiHture. 
Tlio loant trueo of inoisturo in tlio lagging may 
produeo serious loss t>f Imiit by ovajiorjiiion. 

Utigncuili about IH'10 nmdo a carofnl study 
o tho Jlethod of Mixtures, and Iiy wldll dint 
attention to detail he obtained by nmnm if 
it a valuable noiion of thermal data, It in 
only within comparatively recumt yearn that 
any material improvements on Bogmiult'H 
apparatus liavo been offootcd. 

(')) TIIEOIIY or METHOD or MIXTVIIEH,, 
It will lie assumod Unit the wises uniEor eoii- 
mderation urn Mi OHO of Holids and H<jmdn, 
Tlio deturmination of lluv ^[)oui(i<! IKMI(H nf gimon 
rmiuires enpeoial eoHHidtiralion and IH dealt 
with in a Htiparata seetion. 
Lot Mmnas of honied body, 

tf:=tom})oraturo of heated bfidy at tlio 
moment of its immersion in tho 

of tl> (jalorimoter, 
of water omployod, 
4:-= temperature of water when tliebudy 

mimnuMwd in it, 

I 1 ---; temperature when tlio thornwl eipil- 
Ubi'iiun IK t'ntablmliod between tlio 
hitdy and the water, i,c,. wluni 
toinjioriiLuro o[ water iii-uwm to 
rise {or sink if the boily 
than the wnter). 



fifi 



METHOD 0.1' 1 MIXTURES 



Now if H-..-:mtfitn upoeilii; bout of wider lw- 
envu 'I 1 and (, ami M .~n|iomlic boat of Iho body 
i t) mill T, wo got 



Thin tfiveH tlm (raloriinoU'io equation for Iho 
iimtlioil <if luixliiL'os ilk itH very simplest form ; 
for pmcilitsul working mivonil ooiTontions aro 
n in T.H miry. 

(i.) Fur W wo numb milwlitulo another 
W, midli that W|"W-l-imm oE 
1 , Imivmg llio muno heat uajmoity ns eon- 
Htirror, mid nil purls \vhono 
ti)iM|>m'aluro IK mirimmly ud'eolud : 

I.e. if /i -: miisa of tnohi! roaorvoir, Hlirror, oto., 
mid fl[ -.111(11111 Hpeeifii! heat (if this mol.nl 
T mid t, 



\v-w -i-/;, 

jind in thin <WHO (iiwiion (ft) hocomod 

Hr= jyiV-T) 1 ' ' ' '^ 

HniiHitimoH tho subHtunco has tu bo supported 
in a ixinoptiusle, and If wo put ~; water- 

tlio limits of tho oxyoriimmt, wo get 



.. M 

"At(-T) M 1 ' ' ' 
WJioro tins roHiiltfi aro to lio as aoourato ns 
jiuHHllilo, oqufttion (*!) litltoa a nun'o compHualwl 
Cuvii), In luliliUoti to Uio iniiKiiitudca already 
i'(i[ircwont(nl, wu Imvis to tnko ucoount of Uio 
Ihunniil onpacity of Iho tlinnnnnHjtoi'fl, olo. 

In iiddiUfHi to thcsso tiomMiliinift doiumdont 
tin Uio iwituro of thu vnrioim pnrla i)f tlm 
H-ppuiiiliiMj tlni]'^ in tlio (MiolhiR fleirrculion fur 
tlui low <'f linut fi'uni l;ho did 11 ri motor to il 
Hiiri'inindiiif-iH, 

jj (!) MdllKUN Al'l'AltA'l'Urt ]'(> TKK M.KTUO1) 

ot 1 ' ,M!XTIIIII:H.- --'i'ho (tunijilold on Kit niqnmsil 
for ox])irinn'ii(H wlHi Uio inntlitHl of tnixturcH 
cniihihlH of lli following nloinoula, wliioli will 
IID uoiiHidovt'd individually : 

(i,) Tlni oulnrimotrio vossol ami Urn dovico 
fin- mixing Uio auiitoivte. 

(li,) 'J'lici jtmlait oiuiloulng Uio oaltmmolor. 

(iii.) Tlio UiotiiKHiiotoi 1 for nioafluriiiK Uio 
iDinpwniliira i-lwi of the wator. 

(IvS) 'J'lio ninilltmoo for liwilinfi or cooling 
tlui dlmi'Ko (in H])i!ii5ll lioiit (lolormhwllonB). 

jj(0) (JAMH11MKTMII AMD HTIItRXII. (I.) '/'/ifi 

<}itlorim<'i(!r,-'M\Q milorimolor IH usually mndo 
df pnrn wnppor, nlolcol plnfoil ivistt jitiliBliod HO 
ritt lit n.Hlinso nuliiiUtm lo a minimum, 



Tfm HO (if a viMnintn frtokul IIH ft onloi'l motor in not 
to Ijo reeoimiLtwk'd for oriliimry work. Undoubtedly 
Jl IH ponHililo \>y inonm of it to rorluoo Uio mngnitmlo 
of Uio QooUng rule, but thin mlvmUagu i more limn 
by llm (llBudvimLngOB ot this form 



( 



*''** 



f 



'* 



of I'lmdiiimr (inn ID its britllonosa, tliw lujy 
]ioi'|.i(i!in of tlio glafs wnlls abovo tile Hiirfaoo 
water, Uiodilliuiillyof aHecrtflmingits ln;ii.l. cuniiv 
inwl of kcopinjj it cotmtimt. 

Under (iortain oircumstiimses tlio nsii 
walot' or othci 1 caloriinotric fhiid bncomuH 
]>nu!tioiiblo. lU'-iKH) sonio invMtigat 
eniploytid as caloriinotcr t-hiok-wallod iiH'liv""'' 
oiijis nnd truatcd to Iho high cocflioi^nt of !I*' L| ' 
conductivity oE tho metal to cqimliso * '*.** 
lo])i|ioraLure. Tluwi siicc'ialiscd forniw of onl< ** '" 
nmlora aro dose ri I UK! Inter. 

(ii.) The, Slirrer, iStirrot'H vary eoimidonv' ''. v 
in diMgn according tu tlio flpcciflo purp* **'"* 
for whinh they aro rcquirod. A typi*' Jl ^ 
fiu'in IH illustrated in .I'ii;. 1 ; hoi'ts * "" 
K(irt\v ia employed for utiiTing Uin oimto*** '*' 

TIlO VCHHol in (lOllHtl'lHllCl! Wltll llll CO - 

(H'oHa-sdolimi, Iho Hlirrur buing (lontaiucd 

tiihii which in connected 

with tlio main tube at tho 

top mid bottom. Jly this 

arrangomont it if) iuwmblo to 

miaiiro a steady circulation 

tliroiigh tho caloiimcter, ami 

it IB iidviHiiblc to direct tho 

strawn oa nmootlily us ]ioa- 

siblo by suitably curved 




In tho design of fuioli 
flalorimolor partioulav at- 
tontion must ho givon to tlio 
provision of wido passi^ea for tho csirmilH,l-i*n 
of tho wator and oaro tiilcon to avoid an fjii" 
(w jxiHHiblo dead apixces. It might bo re- 
marked tliat thifi mothod of stirring him lM-t*n 
(inmd to bo tlio miml rolialilo for conipiirln* m 
untlis for morciiry thoi'moniotom mid in nni*'li 
Hii]iorior to a plain nerow in a voaaol of liq.iii*l. 

Whito i adopttid a Honiowluvt mmllar t'*tnn 
of oalorimoror for his oxporinionlH oil l-lit* 
B|i(!oillo heat of Hilioatos at high tonijicratii rt>n f 
Tho oliargo, contained in a platinum orimi lilt*, 
waft dni]i[)od (Hrcclly from tlio fiirnuoo into t 1 1* ? 
cnlorimotor. 

It will bo oliBorvod from Fiy. 2 thal> l-lu> 
covor W in in actual contact with the \vn,tor 
to onHuro tomporaturo o([iiililit'inin. Tho tin- 
niilar Hpaco imdor tho covor pormits tJo \vi\t * > r 
to vary Homowhafc in mnnuiit withtmt <iv<i'r- 
flowiiif* or failing to wet tho oovor, wliiln tin* 
woighli of tho oovor (70 gnu.) proven*-** it 
from bring floated out of tho place wlmn II it- 
water IH high. An apnroximato prclhniiiti r,y 
ftdjiistmont of tho amount of wntor is of t ti ivs.*- 
uoooBHnry, and in very easily oblainott. l'Iv*ij- 
oration through tho joint is about 7 mpr. mi 
hour, which is notlikoly to prodiico npprmilft'l,!^ 
orrnr. An oil seal gives very littlo troul>l(, 
and is uaotl whoro maximum noonmoy ( rt 
(loairocl. 



' "Somo Oalorlmotrlo Apparatus," 
Roc. 1010, xxxl, Mo. 0. 



I'fw- 



OALOBTHKTUY, METHOD OF MIXTURES 



(I.) Alwoi'li.ul muinLura if Ui surtiico fi hygroseopio. 
A 1ni'iiis!inl (!ot)]ii-i- mirfiuii 100 mil. mi\um in nn-n, 
will iiliHorli 7 ininifeminK nf water in n Batumi CM 1 
nLiiUMplutrn nt ui'diimry Iwnporatuvc, wlnilsl 11 sia-fnco 
of [loliuhttl niokel of 'tho name ni/.n and imdor tlio 
HIUIIO <iinilitiotis will uot absiorli ns imioh an 0-1 
milli^nim. lli.'iini; it in nlwaj'H advirtiiblo to provide 
tlui c'liloriinulc-r with n lid, altliouKJi il will bo found 
Unit In li> tlio i:iil(rimiiU>r wll'coliviily tlm addition 
f 11 III compliea-tiw llio conslrnutma. 

I'lvcn with t!in Hiinplr-Ht form of appamliiFi a 
uiilndmMid imjmivwiKsnb is jmiduced by providing 
11 liil {if vory lltin iniiUil havJujj ft slob to allow of its 
lioinn nsinovcul for Uio inlrod notirm of llio hot liody 
willwiut dwliii'biiiK tlw t kormoiiHilor. 

()S) TlIK jAlllti'iT HIIIUIOUNDINC! 'J'IM'3 OAf.O- 

uiMKTJ'SH. While 1 (luring tlio ourwo of his 
oxlondud rcHoiivt sites on tho upeeifio heats n 
tho MliisaUw htta dovotcd nnwsh nttontion to 
the ilemgn of tho 
iHiloi'imutrio nji- 
p ii rat us oin- 
jiloycd. 

()no form i if 
juukot for main- 
lainiiigaomiatant 
011- 

aroimd 

tho euloriniotcr 
which ho has do- 
Heriberl in shown 
in Fig, (i. Tlio 
jaokut is ftlunvn 
in Bootion and 
also in top view, 



l-'ui, fi. 

iht1ioto]>sl 




Wtitou is held up 
in tho two halves 
oE tlio cover, and 
i n t li o u i) p o r 
> I* ho 



. 

H, hllmir iiulliiy} .Kciiii 
|ittMH!i)(o of UiurinnuMiOtrji 
iiKiiuiituL-; W, water luvel. 

wutoi 1 tlividoa imd 



H uro. On leaving 



Ul(J ]mjl)0 i| ol , 
noross llirough tlio 

IHi'flo upliui' i)aan]ica ami thon votwrna throujjli 
tho lowor Hpiwo, Itii eiroiilftLlim ia <lirootod by 
bhu parUttons P and Q, of which (i HIIIH nearly 
thn whole length of tlio limk uutaido tho 
aa slmwn by the dotted lino. Tho 
i9 nponcd by moving tho covers 
llioir down-tuniod onda tlion movo in 
tlio U-iiitghs loft at tlio oiulu of tho tank, Tho 
oovors wlido upon the stout rod T. Tho puttoy 
[or tho (laloiiimitor sLii-ror, and tho "\vholo 
jiviikut sliu-op, arc horno on one half oovor. 
Thin linlf in oliiinpcid iirnily in place during ft" 
olwni'vatiiHi ; iiuiviiifi asidti tlio other fully 

'H tlw (tnloi'i motor oponitig- 
(i.) HfclAail of .mppmliny Ilia Calorimeter. 
llimt transEov Ixstwocn tlio oalfmmotor and 
il-H jaokofc may take plooo hi four ways 
1 hoe, tit, 



liy condiKsfcion, convcisUon, radintion, lltlt j 
ovaiioniliDn. Tlio tihjcct of apnlyins the cu >< *" " 
ing con-ctstkin in to cliininnte lliis lioat I* **" 
fi'om this linivl result. 

Whilst in practice it in nut ncocssnry *'* 
study tlicso effects separately, it tni^ht lio 1 ' t *' i 
marked that under ordinary cjcmtliiiniiH i-l*' 1 * 
greater portion of tho heat transfer i* cltu 1 ' *'* 
convection and air conduction, tho two tojjfot-l ' t * 1 
odnsLltuting jthcmt 80 per cent of llio tnUil- 

'It is advisable to roduco tho tnmn[ir **- % ' 
thermal conduction through tho mippnrls* "* 
tlio calorimeter to a minimum HUKJIJ it 4'*" 1 " 
Htitutes an iincontrollahlo Hunreo of ornn 1 . 

Consider, for exam pip, tho CHHC uf a L'iili* rl ~ 
motur supported within tho onoluHtirn <i* l *; 
sheet of tioi'k or ruhhor. When thn csalurjnn'1 *"'' 
and enclosure aro at two steady Uimpwati^ 1 **^ 1 
tho heat tmnsfor is, by tho IIUVH of i!omhust.L< >*|. 
proportioniil to tho teinperrttnro difiure'imci ; 1 * 
however, tbo toiiiporaturo of tho citiUirim^ ****' 
is changing rapidly tho rate of tranter in m* *' 
oven a|)pi'(*xiniatcly pro]>ovtioiial to tlio i*'* 11 " 
poraturo di^renco. 

The following ia a diocuKHion of this mini 1 *"* 1 
of error by Dioldnson : a 

Sinuo t'hc conduotivity of Hiieh miilmin-H* " 
ahvayn small, compared with that of *-|"' 
mctallie slutets in contact with thnnu tJ- 
tomiioiuturos of tho siirfaticn mivy Im lulc^-'Ji 
for the pui'pnfica of this dismission, IXH njiin'ttx i- 
matoly tlui namo as the measured tt!ni|)(H'iil.i i'*' !1 
of the oaliH'i meter and tho junket i'OHjieioliv*'l.V. 
Tho (liHtrilintion of loinpoiuturo in Hiich u hi-y t-r 
and tho nito at which heat in IntwinM l " 11 ^ 
oalorimetor at any timo may ho them lioU.'i 11 - 
mined from the following coiiHidonvtionrt ; 

A sheet of malerinl of thichiioHH c, lioinulol *'.V 
jilauo Hiirfin!*'.H a'o and a 1 , w iiiitmlly at twiinnrnl-ui-n *'. 
H .!<, and nrc Oftoh Inkon UN (t for (nnvciiitniiu'. * >i 
tlio temperature of ono of the mirfmu-H *\ In llM'H 
muswl lo rino from C to 0' in mush iv \my lluvt 
0-0'(l~e'""'), the lompevalni'ti (llstrilmlion iti Hif' 
plato i given by llm following cctiiutlon : * 



IV" , mirx 
i-sln 



A) 



Whom fi a In Iho thcrmoinctric conduotlvity t>f 
mntorlal. F(') ta tho lompuruluro of HIM fwH .-*- t 



Tho point of interest in llttB diHiuiBi()ii J H" rm,l4> 
nt wliioli hoat is tawinf! tho eiilorimolw ul> any 1 1 , M ., 
ns tills dolcrmincs tho valuo of tho cm iw*i v U->- f , , r 
tho portion of tho surface in qm-atlcm. -IT t.t r ,itt<\ 
o nro each mado unity, and the alwvts BSJIR-HH 1 1 i* f ( .v 
ia diftccontliilcd with reaped; lo a;, tho fi>Uovvlnn 

1 Oombiiatlon, Calorlmotiy, nml t'i - 



* " Combtistion, Calorlmotiy,,""'! tli -.HI-H.IH 1t f 
CombiiBtlon o Ciuio HiiKar, Boiuoln *\* i*ii*l 
Nniilithnlono," Sei. Paper Jiiir, Airfff., nu,|, js,,,, 

wr's Series )irf Spherical Ur>ntt tt f rtt , 



2 HO 
1 ' 
p. 110, 



CALOUIMETRY, METHOD OF MIXTURES 



ex,,r^ion for tho tonipomtnrc gradient at any point 
ni tho nnitonal m found; l 



-I- 2^ ( - 1 }'" OH nnrxla 

1 -a 

Tho Hiirfutm ,r-1 i.s tlm mtrfnoo In contact will! Ilia 
culomimlnr. HI) Unit milwtitutiiig tlm vjiluo of x 
mid llin upimipi'iato mint* for and a, Iho uljovo 
oxiircuHioii R [vi!H tlio lompomluro gradient in tho 
iniilMiiil in oondi.it will, the cnlorimoter, which is 
pro |irtinmil to tlio factor k for this portion of the 
' 



AH nil cxftiniilo Hlimving tho effect of tliia kind 
of liidtvihulion of nmtorinl, miripaso that tho onion- 
motor rcslH on a uliool of obonito l o m . tliiok 
and Unit] tlio toinjiomtiiro in ita calorimeter 
rimiH quite approximately neuording to the relation 
0-0<-0-fl- (ji )(0 l -0,). where a -(MM 1 4i(l 0,0 ( , 
and tf, ropivMoiit, respectively, tho temperature at nny 
time, tho initial, nnd Mio final temperature. Tho 
valito of n a , (ho thei'inoinotrio conductivity, for 
olioiilloJH approximately 0-001 in 0,(I.H, units. Tlieso 
ipiiinUliert Hiihstitiiteil in tho above equation show 
that after (10 Hcoondfi tlio nilo of heat IOHN iw 2-7f> 
(<inu>H il.i llnitl valiio, nfloi 1 Ti minutes the lulu in 1-13 
Union tho dual vnhn>, nnd only ufloi' 10 ininuto-s does 
it litimo tn within I pin- omit of \ta iinul value. If 
tlm urea in coninob with mwfi it Bhuot worn a coiiHidor- 
ulilo jutrt t)[ HID ivlmlo area of tho oiiltirinujUa 1 , tho 
nrriir inlriwliioi'il frniu thin iniimo ovitionUy would lio 
n very Hcrionn oai 1 . Kuuli n <!in(.ril)iition of material 
IIH horn dlHiiiiHrti'd wilt alwo havn an oH'iiot on tho liral 
iiiijnmil.y uf HID <!iiliiriiuo(oi'. 

Tlim iliHisutiHinn nhuwu Iliat till no n-cond noting 
Hiip]iinii nliould hit m^lij(i]ily mnull, or, BJIICO tho 
tlicnaiiinotrio cumilnolivJty "K/o/) ( tho ab.soliilo 
ciiiuluitlivily 1C divided by the- miooiflo Imiit (o) nnd 
dniHily (p), tint intiliirinl Hetl for Ihoin wlionlil huvo a 
Hiniill duanit.v nnd Hpnoiilo heal. A form of minpnrt 
Hhould Ihorofom ho wii]iloyod, in which tho mnnllfvit 
piwullilo iniiHH of iiiHiiliiliiif; nia-lci'Jal EH iiwd, with iho 
mnalli^t niitwllito arm in contact with tho caloriinctisr. 
'J'ho imiHH of Huoli inipjHirlfi can rt-ndlly bo iimdo 
iii'HllKildd i!oni])iii'fid wifh that of Iho calorimotor. 

(ii.) MuMMifta ami Npuca Irtwr.an ditlorimeter ami 
Junket. TII ivduro OITOIVI due i tho tilmvo canno 
tu it luiniiiiiini IHi'Uiniiini a ('i))|il(iycd tho following 
nn'an|(t'iLii'iit uf ini|i]HH'tn fin- hix lialoniuolcr. 'J'lio 
itii])|iorlliiL; \i\\w\\ (tlnvn in niiiiilior) nni cuoh mndo uj) 
of a IniiHfi riino niiMon-d In tlui liiitloiii uf Hie jackol, 
nnd a luiinll ivury lip a In nit li nun. in diainolor 
niinionti'd iulo tlio cud uf thu itonn and nsating ngninst 
ttnitiH plud'H (I'lin with a holo, uno wilh IL wloL, and tlm 
Uiinl jilniio) un Mm Iml.lorn nf tlm i'alorim(iU'r. Tho 
Ihoi'iiial (sinidtiiiLlvit.y uf tlio ivory tips IH Bmall, and 
Uii'ir lolid ruiiiifi in not uvci'O- 1 urn,, MI Unit Mioir onVot 
on IliKOixiHiiK 1'itlo inliiii mnull to biixi^iiilioant, 'J'ho 
ImiHti iidiii'.'t, wliili* they huvo n tiotiNidomhlo nmm, 
Iiavn 11 liciit (iiintlui'llvlty I'D Ki'i'til. eiiinpiiiTil with llio 
aiiioiint; of heat v/Mf.h tlioy cnn vfoiivo liy radintion, 
iiuiivouliim. olo, (uliuiit (I'CHIOI cahirlo pi<r Hijiiaro 
liontiniolro |)i-t p mjuniid JUT ili^iro li'iiipi'i'atiiro illlli-r. 
mice), Miat tlio! t' lompMi'iituto in nl, nil limcit iiu-Hniir. 



1 Viiliin fuinul liy i 

lurliui'li'r. 

3 IM. vil. 



liy lUt-Klnsnii fot his 



ably that of (ho jacket, hemx> their effect is entirely 
negligible, both as regards cooling rate and Jicafc 
capacity. 

(lii.) Heat Conduction alony Ihe Stirrer. Tho ateel 
alirrer nhuft which enters the calorimeter should ojicl 
just nbovo it in n thin rubber sleovo, which BhoitM 
fit tightly over it and tigdtly within n larger wtccl 
picoo coupled to tho driving shaft. It ig evident (hat 
since the heat condiiotivity of steel is many times 
greater (linn that of the haul rubber sleeve, tho 
temperatures of the. two metal parts will remain 
very nearly the annie as the temperatures of tho 
calorimeter and tho jacket respectively. The heat 
capacity of the rubber sleeve. Homo of which flhonkl 
be added to that of the calorimeter, IB infiignificatit. 

g (7) METHOD or CALCULATING THE C'OOMNO 

ConiiECTJON. (i.) Sumford. 'RnmioiA vrtia 

tho first to introduce n method of correcting 
for the heat loss from tho calorimeter. His 
procedure wns to malio a preliminary experi- 
ment to ascertain approximately what tlio 
rise of temperature would bo and then to 
cool tho calorimeter half this number of 
degrees below tlio temperature of tlio BiuToimd- 
iiig atmosphere before tho next experiment, 
.for example, let 

Tem|)ora.tnro of atmosphere = i, 
Approximate inorraso= 20. 

Tlio oaloriinotor in cooled to (t-0), mid tlio 
heated body tlum introclucod : tlio maximum 
toinporaliiro will bo upiiroxinmtoly ((+ 0) f 
imcl Itnmford'H idea wwa that tho amount of 
hcut gained ]>y the oaluiimntor during tlio 
time its temperature was below ( will oxtiotly 
compensate for tho amount lost by it wliilc its 
toinjjeraturo WHS above 1. This ia n-pprnxi- 
ntatoly true, but not quite so, owing tn tlio 
fuel; that tho rate of increnno ol lorn pom turo 
dimiiiishra very rapidly no tho heated body 
and Uio wnloi- approach thermal equilibrium : 
thufl, it may huppon that tlio riao of tompora- 
tiiro from ((- 0) to f will oeour in loss tlmii 
20 seconds, wliilo tlio rise from t to (M- 0) 
will occupy over 100 scconda, 

(ii.) Arithmetical Melliml of compitl iny Ural Lu.ts.- 
A far more nnouriite, but not, n curly so eauy n iiK'thml 
of oomwlion in tlio following: ('mil tlio uttliirinioU-r 
Bcfvcml (lc(fi'cs b;li>w tho oiinlostiiro and lh(i viTy 
careful rwidiugH t inturvnlH of uliont 20 BWMiiulH 
boforo nnd uflur tho intmdiiiiLinn of tlio hot body, 
nnd nlno nffi-r tin; mtabliHlinniiit of thoniukl 
iu liiitwcm I ho hut hoily nnd the iviiti?!-. 
Lot 0, f>i, (la, . . , O n IKI (Im tomjuiniLin'cfi o tlm 
niilori motor nt llio lifj-inning and nt tlm wicl of jn 
(irUicl of, nny, '20 iimmitH cwh bufnro tho iutto- 
ilncitinii of tho luiL.boiIy. 

T.ol /, /j, f a /,,, . . . l n IKI lh l(i]iijicnUureH for it 
]ii'rhuli) of I'fjiml (hiration after Iho IiitirHliictJoii n[ 
Iho hot Iwidy ii|i tit tho rAttihliflliincnt of (humml 
ci[nili!irinni liohi'iwii Dm hot body mid lliw ivntm 1 . 

Lot T, 'I 1 ,, 'J'y , . , 'I',, bn tho tomiioriitiircn fm- r 
iiiinilin' |ii i vi(iiln jiftrr Iho rjilii.blinhmont of thcriiuvl 
ni : l, t nnd r l' ui'o virtually tho mitw. 'I'lio 
iiro ( iihonlil nut 1m Uihi>n fmi tlio muling 



SUSTH0.1) OF 



of tfoo thermometer, bub BlioiiUl lie calculated us 



where a ami w have to bo calculated. 
interval wo have 



During tlio first interval nfler (.lio introduction 
.of tlid iion.(ccl body the moan (ninjiemfare of (tic 
calorimeter has been l-}-lj2, nutl i! we put 
v for DIP oliaugo in Hio tompcratnrfi of t!ie onWi- 
jaotor duo to iia snri'onmlings >vo got for Hie fiivst 
Interval 



Bor tho second 



wlicro <i and # have tho HILIUO valuoa us in ttio expres- 
sion for v t . finally, 

^-('"t-"-*)' 
ua (lint between ^ atitf / 

v /"Wit , , . , , , \ 

Av=*a{ :- - -HI - Vr . . - /,i- 1 -*i. 
x * / 

Tho vtiluoa of and x arc found in lf\o following 
way ; Lot i(t raprc-Hcni. tlio menu toinpoiuturo uf tfio 
teforo the introduotion of tlio hot (jutlv, 



M-m 

so that tun mean value of v^d(if> x) between 
and 0,n ! nml putting t for mean (omportitiiro aflor 
cstaljliahmoJit of tliorennl oquilibritini, 

'I 1 i '|i r n 1 i rri 

, j; 1 H- JLj H- J.jj+ *; -'T 

*l~ - j +r ' , 

niltl tlifi moan valtio of v l **a(<j> t se). 




v-v' 



from whioli 2v can bo oaloulatod, and lionoo tlvo 
coi'rcotcd vnluo of tlio ohanjjo of tomperatUTo of tho 
cfiloviinetar. 

(iii, ) Graphical Method of deducing the Neat 
fsoss, A graphical method of computing tlio 
oooling concafcion is duo to Rowland. 

() lloivlantfs Method, 1 Inatoad rtf finding 
the number at heat unite loat by tlio body 
H'JtJ/o Uto icmjjorottiro of tlio liuiiy in rising 

J " On tlio JJfichnnJrjil KfiiilvnleMt of IFpat, with 
Subsidiary Jlosenrclics im tlio Vnrlutloii at Mio 
Slorcurm! Jrom tlio Air TJicrmniiuitw. ami on (,lio 
Variation of Hio HpocJflo Jfcni of Water, " Pfoeee&faffg 
of Da American Academy o/vlrls (irf Kf.ip.ncfs, 1880, 
xv. 7G-20Q ; nlau Physical Papers, p. -102, 



to ita. maxiimnii vnhio, the hd't ' 
accounted for if tho temperature ' H 
whioli tlie hody would huvo 
had buoii no loss. Tho 
aa fullowa : 'First make 
nioiifs of tlio toniponitui'o i>I tlio wi 
calorinifitoi 1 , hefm'o find nflur t.h^ 
dropped in, together with tlin t'in 
plot thorn graphically cm a lut'fC" f 
F-ig, (i. !L^ivc or ton 

f /so 




BiiKicieiit. )i6ci( is tlio 1' 

of: tho wutoi 1 of tlitj 
tho time being plotted Imri/.onlal 
tomjioi-ftturo vortinally. (!mitim: 
dc until it moots tho vortiml lint 
a lioriKontiil Umniyh tho imiul 
point 6, tif tho curvo, di'aw iv 1 
also a vcrtioal ]jn  lay // ( 
and draw tlio lino fbk thi'Dii^'h f 
which indicates iho loi[nii'uii 
atmoaphoro D! tlio vatso] HHIT* 
oaloj'imotor, Braiv ft vortiwil j'A 
point A'. Ifroni tho point of irtnxi 
ft lino j pamllol to dm\ wlinro 
will tlioii bo tho required jKihit. , 
rjao of tomporaturo, 
oorrcotoil /or all oool- 
ing ortws, will 1)0 kj, 

This niofchud, of 
OfflJi'so, only applies 
to oaso where tlio 
final tomporatiira of 
tlio oftlui'iinotcr is 
greater tliaii that 
oftlioaici othorwlso 
tlioi'o will bo uo 
maximum . 

(6) Ferry's Mctfiod. 



f 




If] 



Tn (,! 

maciifiaatum by iroi'ry of KitSvIi 
thia tompoi-atui'O can bo obtniti 
approximation, hy a simjilctf ^ 
ati'iio Hon. 

Let roprcaonfc tho tomptiratv 
rouiulinga, and lot a body afc 
bolcnv thoso fao givou a quantity i 
tiiat its tomperatiirb riaos U> a \ 
Tho way in which tho 
boforo tlio heat H ia 
hy tlio lino AB in Fig, 1. 
Iiow tlio tomporaturo 
is absorbing tho hoat H. Jt'r<.i) 



CAr.ORIME'l'RY, METHOD OF MIXTURES 



liody in, in addition, receiving heat from tho 
surround i i ign, and from to .1) Is lowing boat 
to the HurroimdingH. Tho lino 1)1(3 imiieatios 
the tompuraturo changes duo to radiation, 
otu., alono. 

Througli draw a vortiiwl line. .Prolong 
I'll) backward until it cuts tliia vortical in /. 
1'rolong All forward till it outs tho vortinal 
lino in h. Then the temperature changes are 
fj;ivon by /(/. 

To m> that tho above method of finding the 
draired tomporatimi in reasonable, consider 
the following: If tlio heat 11 had not beon 
t-jivon to tbo body, it would have continued 
to rise in tomporaturo in tho sumo, way that 
it was rising from A to .U, HO that by tho 
timo it roally attained tho temperature 
indicated by it would have reached tlio 
tomporaturo indicated by h; that ia, while 
Lho body really roso in temperature from B 
(,o tho risii in tomporaturo from H to k 
was duo to heat from tho mirroundiugs, and 
Mio rise from h to (,! was duo to a part of tho 
boat H. Again, if. tho body had not beon 
I4ivon tho heat II, but if it had boon at (irat 
lit Him! i a tomporaturo that an it cooled it 
roaohod tho tomporaturo indicated by I) at 
Lho sumo instant that it roally reached that 
tomporaturo and thereafter cooled as shown 
by I)K it would havo boon at a tomporaturo 
/ at tho iimtnnb when it really was at the 
tomporaturo 0; that is, while tho body 
really roso in tomporaturo from to .1) tho 
fall in tomperatiu'o duo to radiation was tho 
Jail from / to J), no that if thero had beon 
no loss of heat by radiation tho riso of 
temperature during this time would havo beon 
from to /. It, then, thero had been no 
gain or loas of heat by radiation tho body 
would havo risen in tomporaturo tho amount 
indicated by tho distance from h to /. 

While- tho tomporaturo of tlio body I-OBO 
from to 1 ) it was roally at a lowor tomporaturo 
than if it had been cooling from / to D, and 
BO did not really lose as much heat by radia- 
tion as ban above beon supposed. Hence, 
tho point / is higher than it ought to bo. 
For a similar reason h is also aomowluvt 
higher than it ought to bo. If tho timo from 
Jl to in about tho name as that from C to 
]>, those two errors will nearly balance oaoh 
other. 

(iv.) Adiabatia Methods. To eliminate 
entirely tho necessity for correcting for tho 
heat transfer between the calorimeter and its 
jacket, 'J.'. W. .Richards L has devised various 
forms of calorimeters in which tho bath 

1 Joiirn. Am. Ohem. See., JOOO, xxxl. 1875; 
JUclmnls awl Bursts, ibid., lillO, xxxll. '131; 
IMdmrds imrt ttowo, 1'roe. Am. Acad. Arts. Sci. xllx. 
'173 ; lUiihfinlB nml Hurry, Joitrn. Am. Gliem. San., 
11)15, xxxvli. 003: MneTimiw nml Bmjinin, " A 
Calorlmi'icr for MonsiirhiK Ileala of Dilution, 
Jonni. Am. Oliem. fine,, Del, 1017, xxxlx. 8110. 



surrounding tho calorimeter ia kept through- 
oat tho experiment at an equal or equivalent 
temperature. This device has beon found to 
bo particularly convenient ill experiments on 
boat of dilution, heat of reaction, and recently 
it hna boon adapted for fuel calorimefcry work. 
Tho precise method adopted for heating the 
jacket to keep it in step witli tho calorimeter 
varies, iliohards baa used tho heat liberated 
by chemical reaction of tho same character aa 
that under test in tlio calorimeter. JjVn 1 moat 
purposes, however, electrical heating ia tho 
more convenient. It IN usually necessary to 
make a few blank experiments to settle tlio 
relative values of tho em-rent, HO tho method 
linds its greatest field of application when a 
largo number of experiments havo to be 
performed, Since the stirrcr in tho calori- 
meter generates an appreciable amount of 
heat, it is convenient to keep tlio tempera- 
ture of tho jacket at a temperature of a 
degree or ao below that of tho calorimeter, 
so that tho residual heat loss just balances 
that generated by tho stirring. Whilst tho 
device cannot givo greater absolute accuracy 
than that in which a stationary jacket 
temperature is employed, it baa the 'ad- 
vantage that tho initial and final tempera- 
tures arc stationary and honco inoro caaily 
measurable with resistance thermometers than 
would bo tho ease if tho temperature wore 
moving. 

(8) TmaiMOMETMll I'OR MEASmiING TUB 

TEMPMBATUBB Jiisn or THE WATKB. Tho 
most generally used instrument for tho 
measurement of tho temperature rise of tho 
calorimeter is tho mercury thermometer, but 
in work of precision tho resistance thermometer 
is to bo preferred. 

Experience baa shown that tho inherent 
defects of tho mercury thermometer limit tho 
possible accuracy to 2 or 3 parts in 1000 
for a 2 rise of temperature* while with a 
suitable resistance thermometer outfit ton 
times this accuracy may bo obtained, but 
of course it necessitates an expensive equip- 
ment and more labour with the observations. 
]?or a discussion of calorimetrio mercury 
thermometers reference should bo made to 
tho articles on "Thermometers" and "Re- 
sistance Thermometers" respectively. 

(fl) APPLIANCES FOR HEATING OB COOLING 
THM CHARGE, (i.) Steam Healer. Kegimult 
in bis extended scries of experiments used a 
steam-jackot heater to bring tho charge to 100 
before dropping it into tho calorimeter. His 
form of heater consisted merely of a boiler 
with a tube containing tho charge, and on 
inverting it tho heated charge is dropped into 
tho calorimeter. White has modified tho 
Regnault heater to the form shown in Fiij. 8 
which is solf-oxplanatory. He employs oleo- 
trieal heating, since then it ia possible to 



CALORB1ETRY, METHOD OF MIXTURES 



move the apparatus about without danger of 
premature cooling. The apparatus is manipu- 
lated as follows : Just before discharging the 
___.. temporary outlet is 
Removable Condenser -+ j 



Th ertaoete 




a*j^a^ag 
Electric Heater' 

Fm 8. 



opened, tho con- 
denser and thermo- 
element removed, 
the opening stop- 
pered, and lastly 
tho heating 

chamber unstop- 
pored, and tho 
charge dropped 
into the calori- 
meter. The objeci 
u-f the ahnlloiv 
below the chamber 
filled with con 
doused water ia to 
shield the chamber 
against superheat- 
ing. White point- 1 
out tlmt tho usual 
practice of closing 
the upper end o: 
stenrn heaters with 
corks is defective, sinco tlio emla aro left com- 
paratively cold, and consequently errors ol 
the order of a few parts per 1000 may result. 

(ii.) Electric Fur- 
nace, For heating 
tho charge to high 
temperatures HO in o 
form of electrical fur- 
nace ia generally cm- 
ployed, as thigpermita 
of tho attainment of 
temperatures up to 
1500 C. It is, of 
course, necessary to 
ensure that tho fur- 
nace should give a 
uniform temperature 
over the region oc- 
cupied by tho charge, 
and experience has 
shown that tho sim- 
plest method of effect- 
ing this ia to wind tho 

., . , tube uniformly, and 

Fio. 0. Arrangement of , J , ' ,, 

IjJittlniirn - -wound fur- ovcl cao11 ollcl ndd 

naco (or Experiments additional coils cap- 




1>, partitions to shblrt ntrol; thon, by ad- 
nKnlustHweooIinB effect of justing the- relative 
IJioofiilsnftlicfiirimrejftS, values of the current 
Hivnifiing shield; L, luteh ,, , 

for dropping out tlio fur- m til0 m(lm circuit 
iwets l>i)LI;om : M3f, lienvy and tlio sun ploniBiit- 
wlrcs for tfm dropping . ;i , 

CHiTonf.,; T, Miermnelenicnt. "'^ c "" s ' ft e 1 
uogrce of uniformity 

can ho obtained. It might be remarked, how- 
over, that tho ratio of the currents in tho 
oircHtta whiuh will givo uniformity at one 



temperature- may not necessarily apply to 
another, and consequently separate experi- 
ments aro necessary to determine tho beat 
values for each point. 

In his work on the specific lieafc nf iliciUes 
White employed a furnace with internal platinum 
winding. This has the advantage of permitting 
of lliu attainment of higher temperatures than 
if! possible with a winding on the exterior of tho 
tube, and also diminishes the lag between tho 
coil and tho chamber, so tlmt equilibrium is 
obtained with greater rapidity. This furnace 
(./''iV/. !)) is mounted on a Htont iron plate, with an 
Air space beneath. An opening of fl'5 om. is cut 
through tho furnace bottom and pinto, wliieh is 
closed by a plug of fireclay carried on a movable 
iron plate. This ia held up against ft largo pinto 



C.T 




Fro. 10. Apparatus of llnrqunrclt Material and 
Platinum for automatically dropping tho Pluti- 
nnm Container, PtC. 

L, latch ; V, i(,s fuluriuti ; JIM, tubes, about -8 mm 
in diameter; \V, wire, whose pull unlatches tho bull 
of the container ; CT, eharRc tiiermoeleiiicnfc; ]?T, 
furnace thermoelement; l\, L',, shielding partitions ; 
II, fnrnaco wlndinB, Tho plallnnm tube around CT 
i tho container la supposed to bo out away. 
L Is 2-3 mm. thick. MM were covered with sheet 
platinum, which was part of tho cciiiipotcnUnl 
shield. 

by tho latch in Riich a way that a quick pull on tlio 
.atch onuses tlio plug to fall away wUluiut tipping. 
Upon tho block and inside the furnace chamber in a 
jcdcatal made up of three fireclay partitions each 
need on both niclea, except on tho Hide facing the 
cmciblo, with reflecting (lisas of platinum foil, and 
supported by a light frame made by grinding away 
as Dinoli as possible from tho thin porcelain tube. 
This pefflestal has two functions. It protects tho 
crucible from tlio cooling off cot of tho fnrnaco bottom 
and it also supports tho crucible during tho period 
necessary to reach tho constant- temperature. Plati- 
num Is very soft at high temperatures, and tho fmo 
wires which support tho crucible for an interval of 
1 second, wliioli elapses between tho fall of tho 
crucible and liio pedestal, would have to bo very 
'a rgo if they wore to hold for any length of time. At 



CALOIUMETUY, METHOD 01? M1XTUIUSR 



(lie liighor lorn perilling l?io ii|)jiniinsl partition in 
iijit to stick lu the bdlloiii of th crmuLlo, .Imnco it 
is'tiw) by pJntinumwirn (" UipplaloLolow, UioivoiKlil 
ot which is enough to pull it luvay. At'ovo llm cm- 
piblo nnutJjor pliitiinim piii'lilioii is mi ape in led. Whim 
tlio pock-still falls from lliu furnnco it is caught in n 
light wooilon box, which cnn lie punlicil out of UK; 
way, and at llic> same time Hwilclu! ail the funiari 1 
auiTont. 

Tlic ftimplcsl iiw.thnd of supiiorUng Uio eliurgfi 
hi the fumnco is to nno a. loop of pluttnttm wiro anil 
tuao it Uy ft strong current v,'\wn it is derived Ui drop 
Clio olmi'go into tlio oulorimt-tni 1 , Tin's method IVUH 
ijacd successfully by HnvUfW ' in liia nsywviiiwiilH i\ 
trie Hjicmlio lioat of iron. 

Wliito foinnl Boino diflimilty with Vim fused wire 
methoil of making a rdwmo nt It'Jnjicmliuva abovn 
lOOO^O. owing to tho (iroijip; wliioh oconiTcil uoros-s 
tlio terminals tiftur tin; wiro wna melted. ThiH 
clifJinuIty oould no doubt liavc boon ovcrooino by 
ninldng llio onrnsiit funo n loiifjth of copper iviro out- 
side tiio fnrnaco tho anino timo aa tlio HH[) port ing 



wire iiii'iilo. lie, liiiw 
ilrn|i fur rHi;usiiig Iliu 



fun n i>f LnlicH niul [ilnlcft, 'I'lid i-dinjihtlti IUTIHIKC- 
inpilt in wliown in /'/;/. II), iSfoitl, |)lnl ililliti win; i>f 
1-2 linn, in diiiniulcr wna njicmlod niildiiiufiiNilly t-ti 
I'i'li'nHo (Ini ^onlniiii']' IIH tin- \v(ii)iJi<n iijiiclfl at llio 
funiaoi) U'IIH Hwnnj; un onu nii!c. Thin wan fininil In 
lin jfctii'i'iilly wtiHfiai'lory, Inil inuriy trmililcH (viv 
(Wonnli'ivti dM'iiiK (o ininiflinii'nt rigidity <if Ilui 
tiiipporl. 1 !, uoi])in<>(l willi (i too r/ijiiil Hieing of lln> 
n hie 111. 

1} (10) 'I'HN >SrU(;lM<! lllvATH <)|i' HlMlfATKH 
A'l' tltdll TKMI'MIiATllHK. ...... Wil-il thll IlllOVO-, 

a|i|mi'iitHH White <J Iintt iniiiln tui 
invi'Hti^ation of tlio limit rnpiioity 
of vtirwHis HilinnliiH ut Jii^.' 1 lotM^iiiratni't'fl. 'I'hn 
data olitii.iii<!(I nro HinniiiiinKtMl in Tnhlo ]., 
from -\vliidi t'Ufi " iimtivHtiiuw> " ntonim liml-s 
Imvo l)(!i)ii ctilinilatcd by Uus jiruc'^dunf ilo- 



TAMT.H I 
INTEHVAI, MEAN AVOMHI 





(I- 100". 


0-300". 


0-51)0', 


0-7110". 


0-11(10". 




IMHIW. 


II- 1. 1(10". 


Silion glflss .... 


3-708 
3-765 


4-272 
4-850 


|.(li!7 


1 -870 
fi-113 


fi'(lll) 


r,'-m 








Crist obnlilo .... 


3-784 
-1-07 ft 


1-5315 


4>lVHi 


fi-OJ3 


fi-m:t 


M?' 1 


Mwi 


fi.'liUl 


Andeaino .... 
Allrito 


4-012 
ft. 5)150 


4 -47ft 


4-H05 


Fi-oflo 


"Sw 


r,Viu 









3-971 


t-17'1 


4-801 




fi-UOU 


n-'i't" 






Microulim; glass . . 
Psoudo-woJlnatonilo . 
Mag. sil. amphiboly . 
Mug. Nil. pyroxene 


4-073 
<M01i 


4-fiDl 
4.7B8 

4-047 


t-l)2l) 

4-l)?i2 
4.907 
f)-0'*l 


B-liJO 
fl.25 

fi-'T)' 1 


r-;m 

8-JJM 


E 


II. IVWI" 
fi-ILMI 


r-im7 






1 






i 


1 ' 


U-imN 


" 



l'A]ir.n 



JNRTANTANfiOUS OK TinTB MMAH Al'OMIO JlBA'i'fl. THAI' IH, IlKATH AT Dlti'lfBItKNV TMill'KUATUHliH 




0. 


100". 


3(10. 


100. 


flOO". 


(100", 


700. 


flOO". 


(HID". 


10110". 


1100", 


1SOD". 


nil 


Silica glass 


A-iA 


t-on 


4-OB 


fi-17 


B-an 


B-48 


5-58 


ft-OR 


fi-7fi 











linurlK 


3-37 


4-1 


fi-1 


. , 


jVl) 


. , 


rHO 


o'fiH 


r.'iiii 


fi.7^ 




, . 


, 


(Wntol)alito . , 


, , 










1"l(i 


fi'5R 


fi.(12 


fi .(17 


fi-72 


fi-77 


fi'H:' 


ii-t 


Aiiortliito . 


;i.74 


4.39 


fi-83 


5-43 


fi-fiB 


fi'lit) 


5-H2 


fi-!)5 


(l.(M 


.Ml 




(1-fi'l 


1!' 












r fi 


- ..., 


r 'IK 


, ,. 












J\lbito 


3-fil 


4.28 


fi-10 


fi-31 


fiIU 


fi -rn 


o-7l 


r..H3 


/>!)! 


r,.'si7 








Jlioroolino 


3'U4 


4-:!7 


fi-nn 


R -;i() 


5-47 


fi-iti 


5-7:1 


/i-79 


/i'NIi 


MIL! 








Mioroolino glass 


3-73 


,[ -;)n 




fi-'M 


fi-(H 








(!!] 


IK1-1 








Wultnsfoiiilo . 


















(Ml 










PBtinild-wollaHlonilo 


:).K 


l-5fi 


B-33 


fi-fiO 


fi'(W 


5-77 


fi.7 


fi-llfi 


(1-03 


11.10 


(1-18 


O.^li 


ii- 


Diopsulo . 


S-8S 


('HI 


R-33 


5-5U 


MM 


r'K;i 


R-tt-l. 


u-u;t 


(HO 


*l-I7 


U.'Jl 






Wag, fiiL am ]ihi l)i)lo 


.'(71) 


1.-I2 


fi 20 


fi-'IU 


ft.(W 


5-7(1 


fi-S7 


fi-IMl 


(MIE 


d'i;t 








Nei'iiBt- liK\inftiin 1 




























formulit for Hilion [ 




, t 


Mlfi 




fi-Ilfi 




fi -r.fi 




fi-(J7 


5-71 


fi-75 




fi' 


glass } 




























(JnnTt.v. nt MVP, tV',1. 





H2 



lwinn Heal tit Iron ut Illidi T- 
. /v, tfs . A'on. six. ; 1'Ml. Mag., Dot, 1110"., 



' J "MMli-ati) Hpin-illii llcnt.-t," fir. 
./i)m, o/ iSVuVw*, Jan, mill, xlvll. 



VOL. 1 



CALQRIMKTRY, METHOD OF MIXTURES 



For convenience tlio values arc given an 
atomic heats, but can, of course, bo readily 
converted, buck into specific heata by the, use 
of tho data givon in Table III. 

TABLE III 
MEAN ATOMIC WEIGHTS, o:t Moi,nnui,\n WKIOHTU 

IlIVIUKlt [IY THE NUMUKII OF ATOMS, V8KO 

AS Mui.Tii-r.iKUs TO uniiuai SrEciFic HEAT 

TO MEAW ATOMIC; HK\T 

Silica, 20>1 

(.'ftlciiiin uictnsilionto .... 23-27 

D topside 21-70 

Aiiortliito 21 '45 

Andcsine 2Q>84 

Natural nlbito 20.33 

Natural iniuroclino .... 21-23 

The method of experiment gives tlio mean 
specific heat over a wido range o temperature 
and ia not suitable for giving with accuracy 
tho truo specific heat, if this changes rapidly 
witli temperature, na ia the caso at very low 
temperatures. At high temperature, however, 
tho relation betwccat specific and temperature 
is practically linear, bonce it is possible to 
calculate tho " instantaneous " or truo specific 
heats with fair accuracy, na follows : 

If tho mtorval specific licnt in sufficiently well 
expressed by polynomial cf|iin1iotis witli constants, 
A+Bfl + CO", oio,, irhero ia centigrade toinpc rut lire, 
tiro total Jient from C. up is. Aft+~BO'-i-V& 3 , etc., 
and tho truo speoifla heat at any temperature, ivhioh 
ia the differential of tho total heat, ia A+2B0+3C0', 
oto., HO that tlio quantity which must be added to tho 
mean speoifio iicafc to get tlio truo hunt Is 



Bui in n- BOrlaa of 4t d-d agree polynomials caoli first 
difference is 



enoh 3rd ilifforcnco is 01)I rt -f 24El l3 tf, where P is tlio 
loinporalnro julcrvnl between ttieli two suMewivo 
values in tlio st'iw-f, It /lloivn nt OHM Hint by milt- 
trading ^ of tlio liril difference from the IH(, 
and then multiplying by OjV, tlio difference of tnio 
and interval heats ia obtained. The method is 
exactly equivalent to obtaining a aeries of 4th- 
degree equations nnd thua computing tho truo 
spcoilio heat, "but ia rnuoh carter. 

For quartz and silica glass tho values of 
tho interval specific heat to 100, 300 th , nnd 500 
satisfy the expressions : 

Quartz 

0-1085 + 0-0001040 - oonooooiitf 2 . 

0-IC70 -f- 0-0001800 - 0<OQG0001250 . 

(11) LOW Tl-MtrKlUTUHB Al'I'MANCES. 
Nornsfc, Mndojimiin, and Knrof " in their 

1 JTcrtiHt, Lfndciimnn, nutl Knret, KUniylMui 
Preussteefie Academic, tier Wt-tsensdtaften za Merlin 
MfMiOwenchle, 1010; ICorct, Aitnalen tier I'fiysik, 
J011 (-I), xxxvl, 40. 



ftxporiinonta at low toinporatiirca conloil dinv r ri 
the aubatanec inidor teat in a (juartv. Vftciium 
vessel, through whicli jwascd. a tuljo o|ii>u at 
both ends, aa shown in Fig. 11. Thin tnho 
was surrounded by liquid air or 
a mixture of alcohol and solid 
G0 a . Tho device is operated aa 
follows : Aa soon aa the equi- 
librium of temperature has been 
Lbio.mc<I it is placed, over tho 
calorimeter. A slide is opened 
iitid tlio contents, suspended on a 
tlu'tstid, are lot down into tho 
calii rime tor. 

Instead uf the expensive quarts 1 , 
vesael tho following simple device 
may also bo used (Fig. 12). In 
a largo teat tube A is placed a 
tiibo J, somewhat enlarged lit tho 
bottom and. closed at both ends Flit. II. 
by moans of rubber stoppers. 
Inside of it is a silver vessel, with tlfo wili- 
stanco- and the thermoelement suspondod by 
a thread. Tho test tnbo is iminci'sod in 
this conetftiit lomporatnro bath. Tho tuni i 
required, to obtain tho equality of tomjiomliiro 
may bo shortened by passing through a nlniv r 
current of dry 
hydrogen, which 
flows into tho outer 
vcascl through a 
small channel in the 
lower cork and then 
into tho nil' through 
tlio cotton-wool, To 
bring tlio substance 
ititn tho calorimeter 
tho whole device is 
brought into tho 
neighbourhood of 
tho calorimeter, 
which is then opened.' 
Tho inside tube J 
is rapidly removed 
from the teat tnbo, 
tlio lower cork taken 
away, ami tho other 
one slightly lifted 
so as to allow tlio 
container to drop 
into tho calorimeter, 
Tlio whole- manipula- 
tion -takes about 
three seconds, In 
that time the sub- 
stance is only slightly 

wanned up. With liquid air, for instance, it in 
olaianecl tliat tho hcufc losa is hardly 1 per cent. 
(12J THE THERMAL UNIT AND TIIU VAUIA- 
TION or TUB SPKOIFIO HEAT ov WATBB WITH 
TUMPKIIATURE,-- It is ciisttunary to oxprctw 
heat quantities in terms of the heat cupaoity 
of water for 1 change of temperature, and 




FRY. MKTIHH) "I' MlX'IVnKS 

Hiiird Ihin heat. ni|ni.'i1y in i\i,\\- l,im\vn iviil h j mil, tun) (1ii> h in^uLf | M , n . , ,.iil,, n 

inuiimuty hi (eritnir uf l|n> jij'imniy iiuil/i ni,' ilrloi mini H| ].\ ,,\< tit . , if I Ii- M,-,.. , I. t i. ; 

rmiliiiH'l.ri', Ki-ain, m<<!,tiil- Jl i-i jH.^iil.jo d, '|' ( , ,,(,! ;J j,, |,,., l( , ,,,!,,,,,.,,, , j,,. |,|, j j,i, ,.,,:. 
li\|mvi;i lli'ill. i|llimlili.';i til 
nf ill! il|i|ili>[)t iillo 



h'nr a Inn;; lime i|. \VIIM linl. fully iriilini'il 



llil|>i*mlmr, innl i'iiiHii'([Urll( ly Illi' |ihili 



whim il liiTinnn app.in'nl I tin) ||u< .itpj-i'iHr 
lintl, 1'iniliJ mil, lin n'[;art[cd .nn mmiinnl d,,, 



JIH'llli'lVI Wi'l'i' fMlll|ll'lli'il 111 IH'jrlv.i) f||,.|n in 
IVlllK'MlDI (if (Hrii' iili.'ll TIllinlHI. 

hi l(i)i'r,V(nivi Ihn win-It nf H,i\vhnnlrt <lH 
ltni'|i>li an. I Mlnu'ciull (1H1II). Ui||iaii>< (l-S 
Liiiliii (ISiKl), I'alli-iMtai' niLil Itiirit.'-i (tl 
linn |inn'.nl cnui'liinivply If nil, Hn> f,.nii nf 

tl|lt'(!ilid Ill'ilf.n'lllJII'I'.Ll.llHt 1'IUVH i; !lul|, ..flr 

ill />'/</. lit, unit Dial, (lii'i-m |M a iMiiiLiniliii v 
al, Ilii" In -Hi" (!, 

IIHi'<> Mm rttfin'ir. l?> nily fully il.'Unml w 
MM* |i,'ii-|lvuliir iH-ivi. (l' : r.) .'.f (PIIII..I,I| 



III III" llhH:i,Llll T ,<t,i till', ll,, 1! . j,n,. '. ; 

'I'll.' jUlnMH:i ,,( |l lt; (),. M.H . I- \- l;t; >,i> J. 
""iri'.l b|l" M.Ul U iS )t, ,1 fl,, ; f- t | . : ,-?,!. !, . , 

lU.-.l lii IIM], , I,, Mi,, i,(, 5 i !,, ,..,., ,.( {, ,,i 

Illlny, IJ,-,.il f.^if..,, (,, ) ^;:, t , n jnj,. (. ., = ., , 

HIP htlt. n in,. ul.,i I'lii.ihu -E l'\ iti> us'' <-t -J i: . t 

'I'll.' ullttT jllln-|ip-li i (*)' hi il 
llni;-Mlm|.,'(t fM E >i...| |,1..,-1, r I ! 



'- 1 ' 1 ' '''it 'I'" ""1-, 'U.L.nL'i. 

ii" fii.i(.<.,( n,.. n.,.1, r . ,-,-, 

ii I;|!MP-I hid,. I!, (I,, ,,,,;. f t ,- h |,j, |, 



1 

U'lHMl 



' "" '">' III!" Hi I' Mill 

MM, ):i. 



ilj'((l.tlii i Hi .ilrl li.'l.t ...-?. 



pninlnl null Hint lln< <II|MI|I<, li|iUvi<i<n 17" .iii.l ll ( i. i-'.|, ( 'i'iMn.|.'-r"^l'- T "''*'" 
1H"( ! , in cijiinl In (hit ini'iui n-alui'lit httfwrtin ll" i ' f i " ( "' * " l "'" 

im.iiu.rNu nmui,,. H,,,,,,,,,, ,.,,,. ,, r IVil)l , P ^-^ 'j )n ;^ _ I;;"'':'.,";;; 

IH'I.UCI'H I / IU1 IH I , HtfMllf la* l'<i||>.|il|.'|'ni| iliii -,,,,.. If f i i 

't miilatilo nnll for uitlnnriii'irv. lr . .1 , ,"' " ! '- v '"" 1 >a I 1 ' 1 '-' 10 ' 
Ciillrntliir it<[<>|i|n jart 1 ., niVt MiMtfxMln IliiiL f ' ^"'j "SVi' l ^ T ^ Vj* *7T' 

";" I ,;;: l i i " rl " |N1 il " (ii11 ;,' 1 '* ^ ^^ ^M i,, ,>!,,;,," i,;,.rr,n'I. i'i" 

iMnmn IMH> jti-mu ul iwili'i-rrnin IU ,V |, iti.fl", ,(, ,11 , , , 

'""< UnyiiniH vitllin liHiv.'i-il I/," nii.t -fr i.f ",] (,' j, ,^" ,' H f '" 



it. null- 



fi>.in ;i i.. ii- 

"'' i'1-n.vn..H..f KM-.^'.iUi,,.,, ;/"..". . ;-v. 

l """ 1N " 1 " lil l-l I -.ltl.i.,1.,1 l (1 ,u. ., ;s ..J : , ,-,:;.,.,, " 

'" ''""> U^i"lr!ln',. i r|.v'.. jT llV,.', ! ,'V.''?.' ','" ','. ii.'. 'I 



., ..... justify h,M 11(t j tl ,;, 



( '' l """'" ni(i ..... ll " v(iriali.,n In ll,,i Itfui .v.im.'ilv 

nf Wltlnl 1 . 



S0:i) -Mr; 

Vrrt.^. A 



,,, 

* IH.H ........ M IIM I (I) ,,I i. v N.,,, Vi ;: 

in. Hint K.M.-f f, ( i', T ,. 1 i(lr l,,^t .I,,;,,,,'.-!,,, 



( 



iM-intU n.iinlih.tlvilv "* ..... M...." if 

1 .* I * i r. 



, 

"" " JS "' ttll! ' 1 ' 1 '^ l - <*" 



<'i"".i...ti. i n;^' i( " ; "^ '" --. '"--. '.- - 



CALORIMETRY, METHOD OF MIXTURES 



to tho nickel - pin ted surrounding vessel ]J 
(Fly. Ifi), The constant. supporting disc forma 
with the iron (if Hie bomb tlic hot junction of 

thermo- 
couple, tlie 
cold junc- 
tion being 
made be- 
tivoon the 
disc a and 
the outer 
vosaol li. 
The M.M.F. 





p. 








16. 



j\, nickel-lined, liom 1) of Iroi!3JMtos. 



tho tempera 
ture of tlio 
bomb is 
measured by 
tho millivolt 
onlilmited to 



Inwolitlit; K,K',twnconstnn(nn;ti8C3 

soldered to bimilj niul to ntekel-tilatcd in oaEoncaon 

(oiipcrsiirroiiiullug vessel ]l[O,qimrta tho assump- 

cnidl)!o - tiontlmttho 

same- weight of inel ift always burnt. 

I'lio itiBlinniDiit liaa uofc yet been developed to n 
stage when it <mn Iso used toe routine testa, BO vend 
source.? of error 
whioli influence 
tho readings 
uofc having Icon 
eliminated. Ono 
important factor 
IB tlie pressure of 
tho oxygon in llio 
bomb. Should tho 
pressure too below 
thnt for which tho 
inutrnmojit linn 
been calibrated, 
combustion will 
^ a " mo lowor 




Mtmrtea 
Via, lu. 

Curve A, prcsijuro of Hfia = ] 00 
Ih. per sfj. inch ; curvo Jt, pressure " boat los" 'ic 
of B(W = 1 fifl Il. iiorHii.inch; curvo 
f), rrt'SHiiro of i^aa = 200 Mi, iirr KI(. 
Inch; curvo 1), ])rcsiniro of giu 
= ariO 1I>. [lernri. Incli. 



to radiation, eta, 

. jii i. B rca(cr 
)V greater 

than tliat midor 
normal oon- 

ili lions. A few typical oucvoa illnat rating this nro 

filiown in F\y. 10. 

(H) Sl'JMIFIO HB-W 1 Olf GAHE3 I1Y TJIR 

" aiETHOD OF ^fix'JtJinos." When dofming 
tlio spcoiflo heat tit a gas it ia necessary to 
specify tho conditions under which tho heat- 
ing taltcs plnco, since tho change of volume 
with tho riso of (ompomturo is eonsklomlilo 
nmlor (iniifltant prcssnro, nnd tlio thermal 
crjiuvfilont of tho oxtornid work done during 
expansion is n largo fi-aotioti of tlio wJiolo heat 
during Uia dtitiigo of tomnoroturo, 
in tho cnso of a gun it is customary 
In spent of two ajujcifiti linats; (I) at consfam't 
volume, nnd (2) nt (Jiia4unt jircssiiro. 

The earliest invual.i^atora tit study thn 
specific boat of gases wore Lavoisier and La 



PJnco, who employed a calorimetrio 
based on tho nicasuromont of tlic quantity of 
ico molted. Later, Bcliiroeho and Bcntrd 
mitdo soino careful oxporimonta in ivhicli a 
uniform ourrent of gjiH, lieatcd at 100 ('., hy 
paasing through a tulie surrounded by a vapiMir- 
jaokot, wm cooled by pafMng through a spiral 
contained in tho calorimeter. Tho inothod 
was essentially that of mixtures, and most 
ol tho subsequent investigators adopted this 
method with various in odifi cations to moot 
special requirement;!. CVnisequently, tho pub- 
fished data uro confined to tho moan spceifio 
lieat over a wido range of tomperatnro. More 
recently CullcmJar and his nasoeintoH havo 
dovolopod tho method of olootrical hoalinf; 
which permits of. tho determination of tho true 
snecHio hoat. 

AmongHt the workers employing tho inothod 
of mixtures Bognaiilt stands ]>re-omiiiont. IIo 
brought to lienr upon tho subject his uniqno 
skill and oxperienco of caJorimotrio monsuro- 
iiionts, with tho result tliat tho data ho ob- 
tained woro accepted, almost without question, 
foe tho following half-contury. Thoro is, 
however, no doubt that tho results given by 
llognaulb wore n, Httlo lo\v, about 2-fi per csont, 
due to an innccurAoy in liis motliod of dolor- 
raining tho heat eondnelcd into tho cnlorimotor 
along tho pipe through which tho gas fliwcd. 
AVitlicnib describing in detail Regnault's a]>- 
paratiis ite cssontial features may bo briefly 
reviewed . 

Tho gus was contained in a largo reservoir, 
heatcil up by passing through a long spiral im- 
moraetl in an oil bath, and thonco led to tho cal- 
orimeter. Garo was talten to ensure a uniform- 
ity of flow of gna through tho calorimeter under 
constant pressure, nnd independent oxpori- 
mont-s were made to ensure that tlio gas leaving 
tho oalorimoter liad cooled to this lomporaturo. 
Binco it was assumed that tho temperature- of 
tho gas entering tho calorimeter was tho fmmo 
as that of tho heater hath, prccautioim havo 
to bo taken to avoid hiss of heat by the gnu in 
passing from tho liath to tlio calorimeter, and 
nt tho e tuna time prevent as far as piwaiblo 
conduction of hoat from tho bath to tho calori- 
meter along the connecting tube. 

Tlic correction for tho heat carried along 
thia tuba, winch was made of low conductivity 
material, wns dt-duced from observations of 
tho chango in tomporatiii'o of the calorimeter 
without tho gas (lowing, This change of 
temperature is duo to tho combined affect of 
tho conduction nncl tlio rato of heating or 
cooling of the oalorimoter duo to the difference 
in temperature between it and tho surround- 
ings. 

Tf A/) IB tho observed rato of change of tom- 
perftliiro per unit time, then A0 is equal to 
A 1W, whero is tho excess of tho temperature 
of the calorimeter over that of tho room. 



CALORIMETRY, METHOD OF MIXTURES 



The lonn A corresponds to the heat conducted 
through the connecting pipo from tho heater 
to the calorimeter, and Bfl to tho heat IHHS l>y 
radiation, etc., from the calori motor. Each of 
those terms corresponded to about B per cent, 
of tho total energy supplied by the gas per 
minute, llegiuiult measured the constant A 
and B by noting tho rato of rise of lomporaturo 
of tho caloriinetoi' before niul after tho gaH 
had piiHHcd through it. Swaiin ' has pointed 
out that an error arises in assuming that tho 
liotit eondnetiim through tho pipo is the samo 
whon gas is flowing as when no gas in flowing ; 
in fact tho hot gas keeps up tho temperature 
of tho pipo in tho vicinity of tlio heater und 
reduces tho temperature gradient. The result 
is that less heat in conducted from tho heater 
into tho pipe whon the, gas flows through than 
when no gas in flowing. Of eonrae a groat 
deal of heat in conducted hy tho pipe into tho 
oalori meter whon tho gas is flowing, but tho 
greater part of this cornea from tho gas itself. 
Tho fact that the average temperature of tho 
pipo in higher when the gas is (lowing nlsn 
results in a greater radiation loss frum tho 
pipo, Tho error acts in tlio same direction BH 
the other, 

Hwann made some experiments to verify tho 
ahove tuiggosllon, and hy attaching thormo- 
junetionti to a metallic tnho he showed that 
tho gradient was affected hy tho flow along it 
and tho results wore of tho magnitude rc<iuirc<l 
to aeeount for tho difference between bin results 
and MIOHO of Kcgnault. 

In Kognault's time thoro was a lack of 
knowledge cimeorning tlio variation of tho 
upcoifio of water with tempera lure, which, to- 
gether with uncertainly as to tho alisoluto 
scale of temporatnro, might also caiiHO an 
error of 1 por cent in hia rcanlta. 

(lfi) VARIATION ov SrEoiuro HMAT WITH 



UANOKR). Hegnaiilt's ohsoi'vationa cover tho 
toinperatnro interval from -30 to 210 and 
presHiiiTH from 1 to 12 atmospheres. Ho fount! 
that tho Hpceifie heat of the gases, air, oxygon, 
and hydrogen wero independent lioth of tho 
temperaturo and the pressure within tho limit!) 
of tho observations. 

Tho ftponifio heat of C0 a , on tho other 
hand, showed a well-marked increase with 
rimng temperature. Kcgnaiilt's work wan 
repeated by Wiedcmann, who confirmed Inn 



Witkowski investigated tho Hpceifie heat of 
air at low temperatures from -i- 100 to - 170, 
and found that the speuih'e heat was indo- 
pendent of tho temperature hut increased with 
Ho worked up to a maximum of 



" Notn on tlin roii(liii;Mnii i\! Ilivifc iilniiK a 1'nnt 
auli which HUH IH Elinvlim In H" Hi'inllou to 
mitfl of tho H]iedlli! Hunt of (IIIHPM," 1'lril. 
., .Inn. L01D. 



70 atmospheres. The variations ivitli preHtiuro 
increased us tho lcii)]ioiutur \vaa lowered. 

Tho method of nuxtn IT,H in not suitable for 
the acciH'iite determination of tlic pressure 
and temperature variation of the spccifio lioat 
(if a g(is. 

More I'oeenti wurk by ohscrvora oinplnying 
tho electrical anothocl has supplied data wliieh 




. 17, 



supersede those obtained in tho above - do- 
soribed investigations. 

HEAT OF fJASKS AT HHIK 
iH. 2 llulbom and AuHtin, 3 and 
later llolborn and Menning,' 1 havoiiwestiguteil 
the speeilic licat ( if gasies up te 1 200" ( '. 
Their method is identical in principle with 
that of llognault'H, but n spcfiiiil typo of 
heater was nwessary for bi'inging tlio gas In 
the high initial temperature. Their appnratiiH 
is shown (Jiagrammatically in Figa. 17 and 18. 




1(1, 18. 

(i.) Arrangement iff Apparatus. The Jlculing 
2 p 6e,-Tho gas wan hunted clwitrloiilly hi a 

ti Kent t, at illi;h 



I'lii/K. Itn>. x\\. Mo. -I. 
Ann. tier J%/)ifr, IIK17, \xlll. 



70 



CALORIMETRY, METHOD OF MIXTURES 



nickel tube A, abiuit a metre long and of 
1 nun. wall tlrieknesa, on which was wound a 
coil of nickel wire. The windings were insu- 
lated from tho tube by asbestos. The gas 
was introduced at one end and was heated 
in the coarse nickel tilings with which the tube 
was filled according tn tho plan of E. 
Wicdomanh. At throe-fourths of its length 
the tube wns closed by a disc silver-soldered 
in place, and the gag was led out through a 
side tubo into the calorimeter. In this way 
tho influence of the cool end of the tube was 
eliminated. Otherwise it was found ont that 
tho gaa in passing through tho cool portion 
gave up so much of its heat that its tempera- 
ture varied in a marked degree with the rate 

of flow. 

Opposite the outlet tube W a second nickel 
tube B was joined to the heating tubo and 
through this a platinum platinum- rhodium 
thermoelement T "'as introduced. This 
passed through the heating tubo A, which at this 
point was kept free from nickel filings by the 
dividing wall M on one sido and a disc of wire 
net on the other. The thormojunction lay in 
tho outlet tube W, 1 cm. from its free end. 
In this space a thin silver band bent in the 
form of a screw was inserted to prevent 
radiation of the thermojimotion to tho aool 
calorimeter. Tho thermoelement consisted of 
wirc30-25 nun. in diameter, which weroinaulatcd 
through the greater part of tho tube B with 
thin porcelain tubes. The hot junction of tho 
thermoelement, which was hardly thicker than 
a single wire, waa left bare. 

Special care was taken that the end of tho 
thermoelement should not come in contact 
with the tnbo wall. In one portion of tho 
work this waa attained by supporting tho 
flexible end of the element on a bit of mica 
of tho same width as tho diameter of the tube, 

The platinum bund, which waa intended 
for the protection of the thermoelement from 
radiation from tho tube wall, also served to 
protect tho cniartu from tho nickel oxide 
which was carried along with the gaa current 
in minute quantities from tho tilings in the 
heating tube. Otherwise this after a time 
became opaque and disintegrated. 

A secondary heating coil of nickel wire was 
placed on tho tubo B, to compensate for 
the loss of heat by conduction through tho 
two side tabes and for tho loss of one turn of 
wire on the main coil where the sido tubes 
wore attached. 

(ii.) 1'h& Calorimeter. fhQ calorimeter 1C of 
abont 0'5 litre capacity was made of pure 
silver O-fl mm. thiolt (Figs. 17 and IS), In its 
centre wore situated three silver tubes 1-5 cm, 
in diameter, filled with silver filings and 
connected by 0-fl em. silver tubes, These 
absorbed tho heat from tho gas as it passed 
through. That the gas actually issued from 



the calorimeter at calmumetric temperature 
even when heated to the highest point (800) 
was mado certain by testa with a constantan 
copper thermoelement. 

Later experiments "by Holborn and Henning 
were made by a similar method with a platinum 
heating tube which extended tho temperature 
range to 1400 C. The calorimeter necessarily 
gains some heat from the heating tube, and 
this gain, in tho later experiments, was partly 
compensated by surrounding the calorimeter 
with a jacket maintained at a much lower 
temperature. 

This compensation wiis found necessary afc high 
tompomturo in order to prevent an excessively 
rapid riao of temperature of the calorimeter: Imt 
although it reduces the apparent magnitude of tho 
ooiTcctiou required, it docs not diminish tho actual 
amount of lieat trannf erred and docs not reduce tho 
uncertainty of the correction. Tho magnitude- of 
the offeot at high Icm]) era. t urea may bo judged from 
tho fact tiiat it waa found necessary, in tho experi- 
ments at 1400 C., to maintain tho jnckofc at na low 
a lempomture ns 40 C. by pausing a stream of cooling 
water through it in order to prevent tho calorimeter 
rising n-bovo 115 C, when no gas was passing. Under 
such conditions tho calorlmotrio corrections become 
HO uncertain that tho probability of systematic 
errors must inorenso considerably with rise of torn- 
poratiu'o. 

Tho rate of incronso of tho moan specific 
heat of nitrogen at atmospheric pressure 
between 840 and 1340 C., shown by tho later 
experiments, was about donblo that found 
in the earlier series, Both series of experi- 
ments could ho represented within tho limits 
of probable error by tho linear formula 



It. appears probable, hoivovor, that tlio value 
of tho specific heitt at C. given by tho 
formula is too low and that in tho caso of 
nitrogen tho rato of increase is not uniform, 
but increases with riso uf temperature to somo 
extent. 

(iii.) Possible ftourcea of Krror. Since tho 
temperature of tho hot gases was determined by 
a thermocouple near tho entrance to tho oalori- 
meter, and tho time of flow of tho gas waa 
only three minutes, Ihero appears to bo aomo 
doubt whether tho couple gave the true moan 
temperature of tho inflowing gas, and also 
whether tho loss by radintion from tho couple 
was properly corrected for. The valuo of the 
moan specific heat of air over tho range 150 
to 270 0. by Holborn and Hoiming was 
2315. Tina is about 6 por cent smaller than 
tho probable value over this range. The rate of 
increase shown by tho experiments, waa within 
tho limits of probable accuracy of the work. 

(17) SPECIFIC) HEAT OF STBAH. Rognault's 
value, 0476 for the specific heat of steam at 
atmospheric pressure over tho range 125 to 
225 C. waa obtained by taking tho difference 



CALORIXIETRY, METHOD OF MIXTURES 



71 



between tlio tutnl licata of steam, superheated 
to these temperatures, as observed by condens- 
ing the steam in a calorimeter. Since the 
cli If eroncc, corresponding tu 100 superheat, 
is only -j'jth of the total heat measured in 
either case, it is evident that the method might 
give vise to largo errors. Fur this reason many 
writers have preferred to deduce tho specific 
heat of steam theoretically in various ways 
from Rcjmault'H value of the rate of change 
of tho total heat of Maturated steam, namely, 
0'305 cal. per 1 C-, which, as Oallendar 1 has 
pointed out, it subject to the same source of 
error in un aggravated form. Thus Zoiuicr 
gives S=0'fi(i8; Perry, 8=0-30G at C. to 
0-464 at 210 0. ; Grindloy, 0-3S7 at 100 C. 
to 0-005 at 1(50 C. 

A direct measurement of tho specific 
heat of steam by Brinkworth, 3 employing 
tho continuous electric method devised by 
Calletidar, gave 8 = 0-484 at 108 0. Subsidi- 
ary experiments by Cailemlar in conjunction 
with Professor Nioolson, by the throttling 
colorimeter method, enabled tho variation of 
the specific heat with pressure to ho calculated. 

These gave the formula 

(O7'J\ 3.3 
~ ~) > 

whom p is tho pressure in atmospheres. The 
approximate constancy of tho limiting value 
0478 of: tho specific heat at' zero pressure 
over tho range to 200 0. was verified by 
calculating tho corresponding values of tho 
saturation pressure, which were found to 
agree accurately with Bognault's observations 
over tho whole range. The theory was also 
verified by a measurement of tho ratio of tlio 
specific heats of steam by Makowoi 1 ,* which 
gave values 1-303 to 1-307, agreeing closely 
with that deduced by Callcndar, 

Tho experiments of Loronz * and Knoblauch 
and Jacob and Ljndo afforded a remarkable 
verification of tho theory of the variation of 
tho apeeilie heat with pressure. They found tho 
specific heat at 1 atmosphere to he practically 
constant over tho range 100 to 1100, but their 
value,, namely, 0-4.08, is decidedly lower than 
Itognault's. 

Holbom and Honning in their experiments 
on tho specific heat of steam at atmospheric 
pressure, improved Ucgnault's method by 
employing an oil calorimeter at 110 BO 
as to avoid condensing tho steam in tho 
calorimeter. They determined tho ratio of 
the specific boat of steam to that o air by 
passing currents of air and steam in succession 
through tho apparatus under similar contli- 

1 Tfrjiort nf JI.A. ffommitlee tm (fascaux Explosions, 
li>(>8, from which tlio nbnvo In nlwtvnntml. 

Phil. '.I'mns. Roy. Sue,, KU5, ccxv. 3B3-'138. 

3 1'hil. Jl/flf/., Fob. HI03. 

1 Forsch. Ver. Dent, Ing., 'llMi, xxl. OH. 

6 l,m. cit. i>|). 1 and 85; 1000, p. 100. 

" Ann. Plios., 100B, xvill. 78fl. 



lions, and obtained the following vtiluus of 
the ratio for different intervals of temperature : 



Tempera turn Interval. 


llatlo/Stcum. Air. 


110-270 
LUM'10 
110-U20 
1 IO-S20 


1 -WO 
1 '958 
1 -{UG 
I '098 


In their subsequent series with a platinum 
heating - tube at higher tompuratures they 
obtained the following ratios: 


Tomiioniture Interval. 


lUitio/.Suiam. Air. 


iiB-sae 

116-1180 
115-132'i 


1-900 
1-073 
2-003 



The second series appears to make tho ratio 
about per cent lower at 110-820 than the 
first, which suggests tho possibility of constant 
errors depending on tho typo of apparatus em- 
ployed or on tho velocity of the gas current. 
The experiments of Callendar and Siviimi 
would make tho ratio 2'OG at 100 C. This is 
higher than any of the values obtained by 
Holborn and Honning at 1400 C. 

Hulborn and .Kenning point out that their 
results at 14013 C. cannot be reconciled in 
the ease of steam and C0 a with any of tho 
results of explosion methods. They are G per 
cent to 18 per cent lower than Langen's, 
which are among tho lowest. l!ut, having 
regard to tho fact that tho constant-pressure-" 
method which they employed appears to give 
results so niuoh lower than Joly's or Calendar's 
methods at ordinary temperatures, and that 
the- experimental difficulties increase so greatly 
at higher temperatures, it does not seoin at all 
improbable that n. considerable part of the 
discrepancy is to ho attributed to systematic 
errors of tho constant-pressure method. 

(18) SPHOIMO HEAT OF C0 a ,- The specific 
heat of C0 a is of groat theoretical interest 
in view of tlio considerable increase shown at 
ordinary temperatures. The table below gives 
tho results obtained by various observers : 



Temperature. 


llcjfiiiinlt. 


WiiMlomitim. 


finimij. 


ITullinrii. 



100 


0'1870 
0-21'JO 


0-10B2 
0'2100 


0-11)73 
0-2213 


0-2028 
0-2101 


Increase 


0-027fi 


0'0317 


0-0240 


0-0133 



It may also bo remarked that the varia- 
tion of specific heat with density observed by 
Joly' agrees very closely with that calculated 
by Cailemlar 8 from tho experiments of Joules 
and Thomson on tho cooling effect on expan- 
sion. E. a. 

J " Calorlinetry. Chnngc of State," G. 
8 PM. ilfaff,, 1U03. 



72 



CALORIMETRY, QUANTUM THEORY 



CALORIMETBY, QUANTUM THEORY 
Tui'; VARIATION ov Sri:oino HEAT WITH 

TMM IMMATURE 

(1) TUB VARIATION or ATOHKI HEAT. 
The discovery by Dulong and Petib in 1819 
of tlio empirical law, Unit the product of tlio 
atomic weight and iho specific heal is approxi- 
inatoly tho same for ail elements, proved to bo 
of tho greatest practical utility to chcmiflta 
when assigning atomic weight values to newly 
discovered elements ; inul further, the simplicity 
of the law directed attention to tho possibility 
of arriving at it from theoretical considerations 
of conceivable atomic structures constituting 
a solid. Tho mean value for the constant was 
determined by Itognaidt as (1-39 with extremes 
of 0'7fi and 5-7. According to tho kinetic theory 
of matter it is easy to sen why a, relationship 
of tho form discovered by Duloug and Potit 
aliould exist. We suppose that tlio atoms arc 
bound together by interatomic forces tending 
to bring thorn to positions of equilibrium 
about which they oscillate j then in this case 
tho total energy of an atom is hnlf-potcntijil 
ami half-kinetic. ; for tho principle of oqiii- 
partition of energy is assumed to bo valid. 
Now in tho ease of a- monatomio gas tho energy 
IB all kinetic, nnd proportional to tho absol- 
uto temperature. Therefore tho atomic heat 
should be half as great in the gaseous state 
as tho solid uta-to. Tho kinetic energy of a 
gramme molooulo of a monatomio gas is jjIlT, 
where It is tho gas constant which has tho 
value 1-085. Honco, on tho supposition, that 
a mnnalomio solid body is built up of atoms 
each with II degrees of freedom, the energy 
content ia JJItT, and from this tho atomic heat 
at uonataiit vohnno is obtained by differentia- 
tion with roapoofr to T giving for tho atomic 
specific- hoitt tho value 3Jt or fi'055. 

It might lie roimirked in passing that tlio abovo 
cqunlion, nouonling to Holt/.nmnn, i applicable to 
tJie caw of oryH tills ii'Iiioli liavo at tlio jiointe of tlicir 
sjmoe. lattice inoluoulen of any dffjrco of complexity, 
provided tliat llio inlomnl forces noting on caoh 
Mom arc proportional to tlio iliatjuioo of (ho latter 
Iroiii its ccniiJihrium position, or more generally nro 
linear tiuiotions o tho ohnngo oC Ua oo-onllnatos. 

Honco tho Dulong and Potit generalisation 
is consistent with tho atomic theory of matter 
and tho etniipartilion theory of energy. 

]"'or nearly a century, however, tho excep- 
tions to tho law carbon, boron, and silicon- 
proved to hn tin enigma which defied solution. 
As far back ns 1872 .Dowar * and Weber," 
working indonondoutly, showed that as tho 
toniporattiri) increased tho specific heat of 
carbon, whether ns diamond or ns graphite, 
oonMiiiieil to anerciiac, Wobor concluded that 
tho spooilio hoat of diamond is trijilcd when tlio 
temperature is raised from to aOO. 

1 Phil. May,, 1872, xllv, J01. ] Ibid. p. 351. 



Jiowar's experiments showed tho spooifio 
heat of carbon between 30 0. and Iho boiling- 
point of zinc (918 C.I waa 0-IS2. 

Some three years later Wobor 3 ])ul)lishc(l 
results nf further ex]ierimonts, and prvod 
that from fiOG" C. upwards the Hjieeilk! boat 
of carbon ceased to vary with incraiHo of 
temperature and became comparable with that 
of other elements. Further, tho diiToronco 
botweoa tho apoeifio Jieat of different miHlifi- 
cations disappeared. By plotting bis results 




100 1BO g 000 

All sola la Son to 



Wobor showed that tho specific hoat tompora- 
turo curve waa of tho form of an old .lOugliuli /, 
Ho found a point of infitiotion For diainoiul at 
about 00" 0., ami that for graphite C. 

lloeont rcsoarohcs have shown tliat tho 
onrvo obtained by Weber is typical of all 
materials when the range of toinponituro 
investigated !H Hiifficiontly large. 

]Jy his development of tho teehniqno of low 
temporaturo research Bowar wan able to> 




pursue tho subject to still lower 
and tlio rowulta for carbon obtained up to 
1012 are shown graphically in Fig, 1, Moro 
recent research by various invoaUgtitora 
employing tho oleotrieal method linn fihown 
that tho general form of tho atomio heat 
tempornturo oiirvo closely rosomhles the curve 
of magnetisation of a ferromagnetic su hstanoe 
under a steadily increasing magnetic force, 
with its very gradual beginning, its subsequent 
rapid rise, and Ita final asymptotic approach 
to a limiting value. A few typical curvoa arc 
shown in Fig, 2, tho O u curve being obtained 1 
by culciilation from O p and tho value of C! fl - C!,,., 
' Phil, Mag, 1876, Sor, -I, xllv. 285. 



OALORIMETRY, QUANTUM THlflOllY 

Tbe results art! given in Table T, 



} Tun QUANTUM Tummy KXJ>LA NATION, 

Hiitjsfaotmy explanation of theso facts- 

forthcoming until tho development of 

'.uaiitum theory and its application to tlic 



"in of speoilio (mat by KhiHtoin, 1 Noninl 

'indemann, 2 .Dchye," and others. 

CJHO physicists developed formulae con- 

ig the specific heat of a solid at constant 

mi with the gas constant H, the quantum 

nut li, tho frequency v, and the alwolut.c , -1"=-" i"""-. 

:*raturc T. JJcbyo's formula involves a ( -'<>l"""i "I. (', cnkmluli'il valno from Hit 



CdJII'AllIHON or TUB UXJ'TIHIMLNTAI. HHHUI.TH WITH 



TUB I'mtlUILAK OF UlS'K'I'KlK, Nr.HNUT AVI It 

LiNniiMAMN, AND DKIIVI; 

(Viliimn 1. 'L', iilmolulo IcniiK'rnl-nrc. 

('oluriin 1 1, (.', from tint Hinuolhcil i-iirvc.H lliniu^li 



the maximum value of the 
which can oiiiuir, 



(Viliitnii lV.--(',,, tiiilciihitcd vuluc from 



tlio formulae quoted I.elow ft is written \ aml , I'"" 1 '*'" rniiiilu (N. wn.l I,.), 

](> quantity A/.li. 

' further details reference should bo made 



3 article " Qiiantinn," Vol. IV. 
j n|)oniu'c boat formulae found uro 



J L 



(10.) 



nity, 



oxprosHion i' is written for r w for 



ojflo huat in measured at constant 
ro, Thus to oiuiijiaro with the Mioory 
qjoriimmlnl rcHiilts iiL'od coirooLing by 
of tlio formula 



n IH the coefficient of eubieal 
!iielticient of volumetric elasticity, w 
tunic weight, / boiug tlm doiiHity. 6 
) Kxi'muMUNTAi. TIM nv VmmuLAK, 
IL. (J]-iflifclin mid H/, t ,r (Irill'itlm tcstcil 
ID vo formulae liy meaiiH of their oxperi- 
1 data for the metids ovor tho nuiL-o 
!. nlm. In .100" (.!. aim. 
y found that no ono of the fonnulao wiia 
In of ropraiontiiiK "xaetly tho oxperi- 
I results over tho entire rango of 
ratlin;, even when tlio values of v woro 
i HI) IIH to lirin^ the csalciilatcd vivbicn of 
toinid bent into coineidoiiiK! with tho 
iniintal values ut imo teiujierature {about 

'. llllH,). 



11)07, xxll. IHO-H(M). 
livr., HMI, |i. 'HM. 
n. il. J'lutx., 11)11!, X\N!X, VH|l, 
i 1 lUro N., N. ft I,., It, ili'imlr MliiHtfilu, NmiFtt 
Kiiiiiiiinii, mill Drhyi' ri'^in't'l 
" TlmrindilyiiiiiiilcH," s (.18). 
il, Trans. ]li>i/. flue. A, 214. 



V. -(', t'nlisulalwl viilun fnun 



Tln> vnluoM of jii- nro j^ivcii at tho top of llus colmnnf*, 



T. 


(' fobs } 


( , (]i , , 


(' (\ tl 










j 




Al.UMINI 


IM. / 


*-m. 


^-.186. f 


i, m -m. 


35 


(l'3!l 


0-12 


0-37 


0-3R 


80 


2 '27 


2-18 


2 -JO 


2-3G 


140 


1 -2(1 


4-2(i 


'1-2(1 


4-28 


200 


ft -14 


R-12 


5.10 


5-10 


2f>0 


ft-r>:i 


r>'<M> 


5-17 


r..47 


300 


f!'8l 


fi-7fi 


fi-7'1- 


5 '7>i 


380 


11.1:1 


(i-03 


(S-Ol 


(1-01 


COPl'KU. flpr=i22%, fil> :>.-.'2tft, fit> m ^ZUi\. 


S!l-4 


0.51 


0-HII 


0-H2 


0-71 . 


H8 


3-3H 


:MIO 


3-74 


It '70 


120 


4 -M 


4 '5 2 


4 .58 


4-57 


200 


5 ->14 


5>4ll 


5"17 


(5 ..17 


280 


fi'HO 


fi-7Jt 


5. HO 


fi-SO 


300 


11-02 


fi-lHI 


(1-01 


ll'Ol 


KINO- fin-^im. ft>>::>2lQ, fivm^lO. 


ao 


fl-Ofi 


0*1 


1-30 


MS 


ao 


1-01) 


4-33 


4-3;i 


4-33 


130 


f-31 


fi-!i2 


5-111 


fi-ltl 


200 


fi-7ft 


5.711 


5-77 


5-77 


280 


0-02 


(1-00 


0-01 


(I'OI) 


MOO 


(i-21 


(Hi) 


((111 


(l-lll 


Wir.vun. f-iv'--.irt1. I'iv.-.'lW, ^i' ,,1 207. 


35 


I-RH 


1-40 


1-80 


1 <).{ 


80 


4-42 


4. fid 


4 -fill 


1-5.1 


120 


0-20 


5-211 


fi'21 


5-21 


SiOl) 


fi-84 


5-711 


fi.78 


5-78 


280 


fl-01 


(Mil 


(Mil 


(Mil 


inio 


(l-lll 


[)>HI 


(Ml! 


11.15 


CADMIUM. /;x..lia. fti< ?-, l,[$, f)it m r.;l<M, 


M) 


11-40 


'.(OS 


4-10 


4-10 


Uti 


5 -110 


5-50 


5 (} 


fi-(il) 


XII) 


f.-87 


5 -8ft 


5-8fl 


5-HII 


iJlKt 


fi-ill) 


5 .|I7 


fi-DI! 


5 >IM 


IMM) 


(l-iill 


-B 


.! 


H-;I.J 



74 



CALOMMETRY, QUANTUM THEORY 



T. 


U,tM 


U,(K,), 


' 


(!(]).)- 


LKA n. 








""2-1" 


~Tim^~ 


3-03 


3 -OS 


2-94 


80 


&-T2 


5-75 


5 -on 


5-Ci 


120 


5-n:t 


5-03 


5-91 


fi-01 


200 


(i-IO 


<M3 


0-13 


0-13 


280 


(i'2S 


(j.Og 


0-28 


(i-28 


300 


tt-15 


6-JS 


(i-15 


0-45 


SODIUM, /ft' = 110. ftv~ln2. fiv m = " 


GO" 


a-fio 


3-87 


3-08 


3 -OB 


120 


5-2 


5-1.2 


fi-ll-i 


5-f)4 


200 


K-17 


6-02 


fl-0-i 


6-02 


>]i)Q 


G-78 


6-30 


(i-3(l 


(i'HG 


3UO 


7-32 


(i-43 


0-13 


(i-13 


IRON. |3v-280. /3J S7U. jSc870. 


50 


0-98 


0-05 


MO 


0-08 


MO 


. 4-2S 


-1-28 


4-20 


4 '2ft 


220 


5-15 


G-2-t 


C-21 


5-21 


300 


o-oa 


5-02 


5-01 


5-01 


380 


a -37 


6-82 


5-82 


G-82 



A'ole. C u was obtfllniitl by cnlcnliitUai from tho 
formulae and the calculated value of Cj,-U aiUlctl. 

It will bo observed that, generally, near tlio 
boiling-point of liquid hydrogen, about 30 
abs., liinsloin'a formula .gives valuta which 
aro too low ; from Nornst and Liiidomann's 
tho values nro tot) high ; while UoLyo's formula 
gives values wlrioli aro in fair agrcomonfc for 
Al, Ag, /in, and Tb, ami, in tho oase of other 
motnla, it agrees with tho oxporimonlnl 
values better thtm oitlicr Kinstoin's or Nonisfc 
and Lmdeiimnn'8. At liquid air tomperntures 
all three formulae givo vnluca which aro loo 
high, 

It is of but liUJu iiso to oiiloiilftto tlio nitpruiirialo 
values of c from (.ho clnHlio cnnsliinls of tlio niotals, 
Binoo Uieso otHwtmilfl aro oiinsidoralily infliiDnocd 
by tho nature of tljn [jroviouu heat tmitinont and of 
tiio tomiioroluro. Hut it might bo rumnrked tlinfc 
tho valncB oalouUtcil from tho olaslio oonstanlH aro 
in accordance with tlioso required by Hio ntoinio 
Jiotvt reaults as shown by tho tlnl* in Tnblo H. 

'JJAIILT! II 



COMPARISON- OF IfjiuQBiimuKa ODTAINBW v OAT.- 

OUI.iVriOM' VROK TUB 1'llVHlOAI, <,'l)NHTANTH 

WITH TUB VALUES ASSUMED IN I)I:HYH'H 



Motnl. 


Al. 


Fa. 


Uu, 


A B , 


(M. 


1'1>, 


t w (ntoinio heat) . . 


8-2 


8-0 


o-y 


1-6 


8-5 


1-0 


m (Rustic oonsttiiits) 


8-3 


0-7 


0-8 


4-4 


8-6 


1-5 



Unit tlio vnliics iibfumi-il fnmi <hi;' Hjiiidiic ln.'nl. 
cqiiatiims am in fair iiyivomi'til "illi U"" oiiluulatcil 
frtim Hie clastic consUiits. 

(4) Al'i'UOATiON Of "DlJHVE'S AND UlH- 

STKIN'S FORMULAE TO TILE NON-HKTALS,-- 
Pure metals afford the most reliable data fur 
testing bent tiioorios, but ^coinjiariHOTia with 
the available oxpwi menial data for eomplox 
substances such as crystalline salts (NuCl, 
KOI, KJJr, AgOl} and diamond aro of great 
theoretical interest. 

Ono difficulty in making suoh comparisons 
is uncertainly in the value of ('-(' owing 
to tho lack of data concerning the clastic 
constants. As data were not available for 
calculating 0,,-CJ,, from tho thermodynamioal 

relationship, 

wttVr, 

P 

Nornst and Lindomimn l obtained apjH-oximato 
values for C^-C,, by a different procedure. 

TAHLK III 



AbHolute 
Tern peril tu re. 





<Jn. 
0,, a TA. 


ALUMINIUM 


32-4 


0-24 


0-21 


35-1 


0-20 


o-:;;t 


BO 


0-20 


0-2(1 


80 


0-31 


0-28 


100 


0-3-1 


O-IiO 


COI'I'BB 


23-5 


o<ir> 


0-14 


27-7 


0-1(5 


O-lfi 


50 


o-ia 


0-1(1 


70 


0-20 


047 


DO 


0-22 


0-18 


110 


(J-23 


0-11) 


SlI.VEIl 


3(1 


0-21 


0-25 


40 


0-23 


0-27 


(10 


0-25 


0-20 


80 


0-27 


0-31 


100 


0-I!0 


0-114 


130 


0-32 


0-JiO 


23 


0-35 


0-1)4 


'28 


(Mi!) 


0-37 


37 


0-43 


0-40 


r>o 


0-47 


0-13 


80 


0-fil 


0-10 


100 


0-CC 


041) 



They Imscd tlmir method of cnlonlation on 
Qrunoisou's obHorvivtion that tho coefficient 

1 La TMorie du rayimnement el les qimntu, 1012, 
p. 205, 



CALORIMETRY, QUANTUM THEORY 



75 



<>f expansion is proportional to tins atomic heat 
in"! obtained tho approximate) relationship 

B -CJ,=C y TA, 

whoi-o A is fl constant charaotoristio of th 
Hll(l!lt icG which can bo deduced from measure 
"junta of tho compressibility and cooflidon 
'I "xpansiim made tit one temperature?. 
Ifc in possible to teat tho validity of thi: 
^I'lUiilae by comparing tlio data obtaincc 
l '>m it with thoso given by tlio thormodynain 
< ! [il equation in the CHHO of tho metals Al, As 
-It, find On (see Table III.}. 
.Nornat tested tho formulae of Nornat aiu 
u and of JJobyo on tho data foi 
and Table IV. summarises tho 



Diamond ji s > 



= 1800 for JJobye'a. 

'1910 for NeniHt and Li ndom ami's. 



Olraorvcr. 




C ;J . 


DUVci-eiiCH. 


i 
i 






Oil*. 


fttri-yet 


(11 is.-c ri It. 


CM. niiiu."f, 


t 
i 


Horns t . 


88 


0-028 


O-0'l!) 


-0-021 


-1-0-022 


1 


11 


02 


0-03 If 


0-0.18 


-0-025 


-i- 0-024 




.. 


205 


0-U18 


()( 


-i 0-008 


0-00 




i 


209 


0-(JG2 


0-Ofi 


-1-0-002 


-1 0-01 




it 


220 


0-722 


0-74 


-0-018 


=0-0-1 




Wisher . 


222 


0-70 


0-7fi 


-1-0-01 


-0-02 


i 


Do war . 


243 


0-05 


0-025 


-1-0-025 


-0.02 


{ 


\Vobor . 


202 


l-l't 


1-JO 


-1-0-04 


-0-02 


t 


3> 


281 


1-35 


1-32 


1-0-08 


-0-02 


j 


X 


,10(1 


I-f>8 


1-6'i 


1- O-0'l 


-0-01 







831 


1-84 


1-82 


-1-0-02 


-1-0-01 




.1 


3G8 


2-12 


2-07 


-1-0 -05 


-1-0-04 







413 


2-08 


2-01 


-1-0-05 


4-0-11 




" 


Nil} 


6 I5 


0-40 


-0-fl'J 


+0-04 





It will bo observed that Bobyo's formula 
VUH nn approxiniato representation of tlio 
:pnrunontal results. TJio Neimt ami 
.lulinnaiin fortnnla gives values which ni'o 
n low between 88 U nncl 02 aljs. In tho 
no of Dobyo's tho {lill'oi-onccs uxeccd tho 
fibablo error of experiment, tho gonoml 
[)iid licing for 3>obyo'n formula to givo 
diU'H whioh aro too largo ut low tomporalurcB 
id too small at high temperatures. In fact 
o duoroaso of atomic heat with decreasing 
ni|)(vmtiiro is more ra,pid than that given 
' .Dobyo's formula, 13waltl made oxpori- 
DII ta on tho mean atomic hunt ol dimnond 
Sa-8 and 104-0 abs. and found tho 
0-2119, HO that; tho total energy 
between the so tempomtiires JH 
calorics; tho vuluo calculated from 
n formula is 20-31, Korof, umjiloying 
calorimotnr tlcsdrihwl in " (,'alori- 
;itiy, -lOloetrical Mothotls," {'**)> f""<l 
e moan atomic hoitt of diamond between 
3-8 iind 270-0 to bo 0-81M, 



Juo 



to nn energy difference of (J5-8, 
formula gives (il-E) cnlnrk'H for thiw interviil. 

PfHyalomic Substances. Tho nictaks and 
diamond aro regarded aa monatoinio struc- 
tures, whilst tlie iiMilcculea of graphite and 
sulphur appear to be compounds of several 
atoms since the atomic heat curve \B for these 
much less abruptly curved towards tho tem- 
perature axis. 

Nernsti > IUIH attempted to apply thoformnlno 
of Dobye and llinstcin to polyatomic sub- 
stances auoh as KC1, NaCl, etc. f-fo assumes 
the heat vibration to be of two types : first, 
tho vibration of tho molecules an a wholes in 
exactly the same way as the atoms ol a 
inonatomio body; and, second, the vibration 
of each atom about its position of rest. The 
vibrations of the atoms are interpreted aa 
giving rise to the "Ilcststrahlen" discovered 
by liubons. Since at low temperatures tho 
vibrations of tlio atoms become much more 
regular, and accordingly tho absorption bnntla 
narrower and more pronounced, it in assumed 
that Einstein's function applies to the atomic 
vibrations. 

Honeo for tho representation of the atomic 
heat nf the salts tho expression is 



in which 1'V ]}\ are the functions of Doliyo 
and Eiimtoin respectively, i^ tlio frequency 
ealeiilatetl from tho melting- point, 2 and r' a 
that found by Itubona by mcaim of the optical 
method, Hiiico thoso Halts nlunv one vory linrj) 
nfra-red absorption band. 

l ( 'oi- details of tho eojuparison with oxperi- 
iiont, roforeneo should be made to tho original 
already referred to. x '. 



^Ar.oitv or CALORIE i 

Tho 15. Tlio quantity of heafc required 

to raiflo one gramme of water through 

1 0. at 15 0. Sco " ThermodynainiflS," 

(2) ; " Heat, Mechanical Kquivalcnt, of," 

, (0). 

Tho 17'5. For some pui'imacn tho ran^o 
from 16 C. to 20 C. in tukim and tho 
caloric defined at 17"-fi. 

Grammes.- One- him drcdth jiart o( tlio heat 
required to warm one gramme of water 
from tho molting-iioint tn tho boiling- 
point at a pressure] of ono atmosphere. 
See n,lno "Thermodynamics," jj (2); 
" lioat, Mechanical Jilquivalcnt of," (i)). 

Pound. A British unit of heut, fioing one- 
hundredth of tho amount of heat required 
to i-aieo one pound of water from tho 



. 
Unina 



he- fSoliil ftlala (Loudon Univ. 1'rcss). 
, l^iysik SScilscli., l!l](), xl. OUO. 
10 hyiiothcsH Mint tlio innlUiiR-]Miint Is 
y Mm Xaist that at Mite toiujmrnturn fho 
r tho vlbi-iitlDiw of tlio lUoim iiniiiml Uicir posltlniw 
rest become eonimcimimito with tlie ntinulu 

IHtlUHiOH. 



CAMS, KINEMATICS OP-CATHODE BAY MANOMETER 



molting -point to the boiling - punt nt 
one atmosphere. Seo also "Thermo- 
dynamics," (2). _ 

KINEMATICS OF. SGO " Kinematics ot 
Miichiiiory," (0). 

CANAL WALLS AND KFFKOT ON STREAM-LINKS 
OF COVING Sun-. Son " Ship Resistance and 

Propulsion,'' (!H1). 
CARHON Droxmn, LATKNT HBAT OF VAI-OMBJA- 

TION oi' j determined by Mathias. Sen 

" Latent Heat," (8). 
CAItltON RlONOXtl)K, Sl'EOIFIO IlKATH OF j 

tubulated values obtained by School and 
House, . Soo " Cnlorimotry, Electrical 
Mothotla fit," (IB), Table IX. _ 

OABKOT'S CYOLH. Sco " Thermodynamics, 
(18), (40); "Engines, Thermody- 
namics of Internal Combustion," (f>). 
Por a Porfeob Giw. See " Engines, Tjiormo- 
dynamics of Internal Combustion," (fi), 
(0), (23) ; " Thermo dynamics," (18). 
For Steam, See " Steam Engine, Theory 

of," (2). ' T 

OAUPBHTIBII - HOSPITAHEII INDICATOR. bee 

"Pressure, Measurement of," (19). 
CASOAnii METHOD OP COOLINO ; introduced by 
Pictet. Sec " Gaaes, Liquefaction of," (1). 
CAST IIIOH. Sao " Elastic Constanta, Dotor- 

niination of." 
Ci-ushiiig Strength. (39). 
Effect of Tomperatuiro on the Transverse 

Strength. (37) (ii.). 
Toiwllo Strength. (38). 
Testing Transverse Teat. (37) (i.). 

CATHODE KAY MANOMETER 

Sm J. J. THOMSON suggested the HBO of Piozo 
Elootrioity 1 aa a means of measuring sudden 
pressures, and the mctJicid lias recently beer 
ivorJced out by Dr. I). A. ICoya." Ci-ystala of 
toiinnalino arc exposed to tho (lotion of tin 
prossuro and tlio nlcctrieal ohargo nequircd, 
which ia proportional ' to the- presanro, is 
moaeurod by a special form of cathode my 
osoillograpli. 

The nmonnt of the ohargo is measured tj 
tho deflexion of a bourn of cathode raya wliioh 
Iiasscs Iwtwcon two parallel condenser platen 
which receivo tho charge soparatcd on tho 
tourmaline crystals. 

The beam ia also deflected in a direction 
at tight angles to this olcctroatntio deflexion 
by a magnetic field applied parallel to tho 
electrostatic Hold by mt-aiia of an altornatinj, 
onrronl; of known frcquciiey, giving a timo 
diaplftcoinoiit, perpendicular to the olootrostatio 
displflcomonL Tho beam falls on a photo 
graphic ylato, thus a chargo time record i 
obtained, and since tho charge is proportions, 

!; . Seo (irtlclo " 1'lcxo IJlMstrlclty," Vol. II. 
' " A HostoolecUlc Motliod of incasntlnK fcx 
';'/!^ May., 1021. sill. -173. 



, the pressure this is equivalent to a 
imo record. Tlio adv.uilago of th method 
in tho fact that the inertia of tho moving 
of the recorder, tho beam of oalhodo rays, 
H negligililo. 

'Hie ftniwratiiH oonflistii of two purlfi: (I) 
ho' pressure vcsaol, and (2) tho calhmln ray 
scillograph. . 

Tho prcssiiro vessel is shown in 1'iy. i. -it 
onsistcd in Dr. Keys' experiments of a IminB 
esacl All, about (i in. in diameter and 1-J- in. 
Iccp elosed by ft i-in. steel plate UK, liohl 
lown by 12 holta. Tho walls of tho vessel 
voro -1 in. thick. A sparking plug L and a taj) 




N are fitted in tlio steel cover. .D13 is a thin 
cad phi to electrically connected to a copper 
wive which passes through an insulating plug 
G in tho side of tho vessel. 

Half of tho tourmaline crystals, about 1 em. 
in thiokncsa, are attached by a little wax to 
tho bottom of the vessel, tlio other ball are 
attached similarly to a steel plate HI. Tho 
lead plate DE separates these two sets of 
crystals, which are so arranged that all tho 




positive faces are in contact with the load 
plate.' There aro 5 or'fl crystals in each layer, 
the area of each crystal being about 12 B(J. cm. 
HI is fixed by steel screws to the bottom of 
tlio vessel. Tlio lower part of tho vessel is 
filled with vaseline to delay the transfer to tlio 
crystals of tho heat generated by tho explosion, 

When pressure is applied above TIL, .DM 
becomes positively charged and tho amount of 
tho ohargo is proportional to tlio pressure. 8 

Tlio insulated wire EGF convoys tho charge 

to tho condenser of tho oscillograph. This is 

shown in jf'% 2, Tho cathodo raya aro 

generated by tho fine tungsten filament If, 

3 T. Curie, OStivm, p. 10. 



CATHODE RAY OSCILLOGRAPH CEMJ3NT AND SAND (MORTAR) 77 



which is heated to incandescence by an S-volt 
accumulator. The cathode ray tubo GG is 
cemented into a brass sleeve BIJ which in 
soldered into a brass cylinder CO tho axis of 
tins cylinder ia ab right angles to tho paper. 
The rays enter the sleeve BE through a small 
hole 0, pass between tho plates JIN of a con- 
denser and then between tho poles WW of the 
electromagnet and fall on a 
photographic plate X in tho 
cylinder CO. Tho plate slides 
in ft rectangular box within the 
cylinder and can be moved from 
outside. 1 A window Y in tho 




005 .01 .010 .02 -025 -O3 -033 - 04 

Time. Seconds 
-Km, 3. 

cylinder CC closed by a screen of willomito 
allows visual observations to lie made when 
tho plate is drawn aside and thus facilitates 
adjustment. The electromagnet is excited by 
an alternating current of known frcqiieney, 
thus tho time scale is fixed. LL is a brass 
guard tube ;J in. in diameter. This guard tubo 
and one of tho condenser plates N arc con- 
nected to earth and to ono polo of a direct 
current generator supplying a constant poten- 
tial difference of from 3000 to fiOOO volta. 
Tho other pole of tho generator ia connected 
through a special double-action key S to fcho 
tungsten filament; the key also 
serves to fire tho explosive mix- 
ture. The second plate M of 
tho condenser is connected to 
tho lead pinto of tho pressure 

5 d- 




015 'O2 ' 

/nnj, Seconds 



03 .035 



apparatus. On depressing the toy S tho 
cathode potential supplied by the direct 
cm-rent generator iy first communicated to the 
tubo; a further motion of tho key detonates 
the charge. The cathode, raya arc deviated 
in a direction at right angles to tho paper 
by tho magnetic field, and until tho charge 
is fired trace a short vertical lino on tlio 
photographic plate. The electrification of tho 
condenser plate M duo to tho pressure produces 
a deflexion of tho rays in tho plane of tho paper 

m',., 8 ' 1 ' J ' n ,f n ,? h n, olllson ' Jfw ' /fl f Positive likclric&y, 
1013, lip. 22-23, Longmans, Uroun & Co. 



and thus the time-pressure curve is traced mil 
tho plate. Tho displacement of llin (\\iot 
depends on (1) the cathode potential and (1!) 
tho potential difference produced by llin 
charge between tho plo/tcs of the comlcnm-i 1 
J\IN ; tho apparatus requires calibrating !< 
those. For tho method of doing this refcroimn 
should be made to Dr. Keys' paper. 

Figs. 3, 4, fi, C, taken by ponnisstoii from Jiin 
paper, give the results of some of Iiiii 
A experiments.; the effect of tho ad- 
dition of air in slowing down tlm 
explosion of H s and O shown in 
Pig. 3 is very marked. With nn 




o -001 .ooa-ooa .011 -oia -oia -oi4..oi6 

Time, Seconds 

irio. s. 

air (cniyo I.) tlio maximum pressure of abniit 
220 Ibs/per sc[. in. is reaclitid in lra Hum (HlOI)ti 
Heconda. With some GO ]icr cent nf nir in Mm 
mixture (cim r o HI.) tho maximum pn-Ksnrn 
U reduced to less tlmn GO per couL of itn furnn'r 
viiluo and the rise continues fur ahmiL O'llllI! 
aecnnda, or some fifteen timra tia long nn 
previously. 

Tho curve A, Jfig. ft, is 
eurvo for the explosion of gnu-cott 

water; it given tlm 
wave, while en rvtOl ifuluu 
to tho ivavo rofleeli'd fj-nm 
the bottom. Again in 
'.'Fig, 0, tho effect nf nlU-r- 

V 

S-20- 



10 20 

Dlstanao fit 
Fro. 6. 



ing the distance of tho cliargo from tho 
vessel is shown. 



CATHODE HAY GsciLi.ooiiAvir. Seo Vol. ,11, 

" Hadio Krcqiicncy Mousufoincuts," ^ (-15). 

CAVITATION. Sco "Ship ItonfMtiuwn mid I'fa 

pulsion," (48). 
GEMKNT : 

Artificial and Natural JTyclraitlici (Vuin-nf 
Tests for Poi-tlancl Coiiwut, Ken " Klii 
ConBtaiits, Dotoriniiiatiou of," (Ilifi). 
Character iatio ^cpiatioita for Tnnsilo TVH(- 
Oement ami Morfcar. Soo ibitl. < Ifi7). 
Sotting Tinio. See ibid, (Ifig) 

OlOMKNT AND SANK (MOIITAH) TKWHi 

TUSTINO. Sco "EUtstio CcumUuitH, .Il^l 
minationof," (lfi(i) (ii.). 



78 



CEMENTING MATERIALS : CLASSIFICATION-COAL CALORIMKT.UK 



CEMENTIHCI MATERIALS CnAssmoATioN. See 
" Elnslic Constanta, Determination of," : 

(NS2). 

OEHTIOHADB SOALE OF TEMCEBATUKE : a. 
ao.ilo, used in all modem thermoniotrio 
work, in which the numbers and 100 corre- 
spond respectively to the freezing- and 
boiling-points of water, in each case at 
pressure of rmo atmosphere. See " Thermo- 

motry," (2-). T , 

CKXTRIKWUL Fr-ujD TAOHKOBIKTBIW : lor 
measuring number of revolutions per mut 
time. Soo " ifotowj," (4), Vol. IH. 

CHNTRIPITOAL PUMPS. Boo " Air - pumps, 
(82) ; " Hydraulics," (38). 

CHANNELS, HYDRAULIC FLOW IN, AND BEST 
DIMENSIONS oi\ Seo " Hydraulics," (27) 
and (28). . 

" CiiAKAcTEiuSTia CURVE " for geometrically 
similar atnioturos of which tho corronpimding 
parts are made of tho name material, and 
Non-din ions tonal Bases. Seo " Dynamical 
Similarity, TJio Principles of," (44). 

CiiAitACTEius'fKJ EQUATION or STATE, Seo 
" Thermodynamics, Definition of," (50) ; 
" for Ideal Gits," (fi7). 

CIIAHLES' LAW on tho expansion of gases 
under constant prcssuro states that 

=i\,(l +al), 

v n and v being volumes at temperatures 
mid (, whoro a is approximately constant 
(tor tho more permanent gases) and is oallcd 
tho coefficient of expansion at constant 
pressure ; it has nearly tho same value for 
all tho mom permanent gases. Seo " Thermal 
Expansion," (14) (i.) ; " Thermodynamics," 
g (fi); "Engines, Thermodynamics of In- 
ternal Combustion," (14). 

CHATTOCK GAUE. SIM " Pressure, Measure- 
moat of," (27). 

CIIKMICAI, PHMI-S. See " Aif-iiumps," (10). 

ClIH/.Y 1''OI1M1I1,A FOE liYDIIAULTC! LOSSISS IN 

PIVEH. Stso ".HytlrftiilioH," (2B) {!.). 

Practical form of aumo. Sou ibid. (2/i) (iii.). 
CiniONOMFmio iHSi'miMHHTa : Ifm monauring 

mimlxn 1 of rovolufcions por unit time. Koo 

" Motora," (3), Vol. III. 
Cr-ATKYHON's EQUATION. See " Thormo- 

dynannca," g (41). 
CLA'KK Gr,f,L, VALUE OF E.M.l 1 . OP. Seo 

" Mcohoniuat Equlvalonb of Hoat," (8). 

See also Vol. II., " E.M.P., Standarda of." 
CLASS VARIABLE : a non-tlimcnsional group 

of torma connecting a class of problems 
sinp; certain geometrical and dynamical 
iities, tlio solutiona of which are ox- 
fi functions o( tho olasa variable ; 

if (,1m pmbhim can l.io expressed in terms of 

a <li(T<iH'iil'ial (-([nation, tho Hulution IB sought 

for art 11- jUMvin 1 HOI-ICS in the class variable. 

Hue " iDynainitial fSiniilai'ity, 'IMio Principles 

of," S (-1*0). 



CLAUDK'H MOIIIFICATION OK LINDU'S METHOD 
i-oii .LIQUEFACTION OF OASES. Scic " OaHcs, 
Liquefaction of," (1). 

Atisius' THEOREM: an advance towards 
tho explanation of the departure of tho 
behaviour of fluids from tho laws of 
perfect gaaes. See " Thermal Expansion," 



CLEARANCE IN STEAM - ENGINE CYLINDERS. 
Sno "Steam Engine, Reciprocating," (2) 

(viii.). 

CI.EHK TWO-STHOKE ENGINE. Seo " .Engines, 
Thermodynamioa of Internal Combustion," 
{), (3*). 

COAL CALORIMETER 

VAISIOUS forma of apparatus have boon 

devised for determining the calorific valuo 

of coal. In practically nil tho selected sample 

of coal is burned 

in oxygen ; tho pro- 

ducts of combustion 

are passed into a 

known quantity of 

water at a known 

temperature, and 

tho rise of tempera- 

ture is measured. 

.Fig. \ is an illus- 

tration of the ItoHon- 

liain colorimeter as 

manufactured by 

tho Cambridge and 

Paul Instrument 

Company, The 

instrument consists 

of two parta, tho 

calorimeter proper 

containing the water 

and tho combustion 

chamber in which 

tho sample ia burned. 

The combimtion 

chamber ia formed of a glass lamp chimney 

closed at the top and bottom by metal damp- 

ing platea, separated from tho glaBB by rubber 

ivashora and held together by clamping aorows 

on three uprights fixed to tho lower plate; 

tho wires connected to tho olectrio ignition 

arrangement pass through tho upper plate and 

alao a tube for the supply of oxygon. Tho 

whole chamber is immersed in the water of tho 

calorimeter. An aperture in tho plate ia oloacd 

by a ball valvo through which tho producta of 

combustion can iasiio into tho water, but which 

prevents tho entry of water into tho combus- 

tion chamber. On tho completion of tho 

experiment tho valvo is raised, allowing uomo 

water to enter ; this ia afterwards forced. 

out by tho oxygen and mixed with tho rest of 

tho water, thus" enouring that tho calorimeter 

and its contents are brought to one tempera- 

ture. To reduce tho radiation JORBCH tho whole 




80 



CONTRACTION OF AUEA AT FRACTURE-DEGREE OF FREEDOM 



CONTKAOTION OF AlU-U AT FliAOTlIHE. fieo 
" l!!astio Constant!!, Determination of," 

CONVECTION OF HBAT: 

Forced. See " Heat, Convection of," $ (1), 

(2), and (",>). 
I'l-oin Fine Wires and Oylindors. Sea ibid. 

g(2)(ii.)and(4)(iv.). 
Niituml. Soo ibitl (1), (4), and (fj). 
COOLING COEHEOTION, MKTIIOD OF CALCULAT- 
ING, JN METHOD OF M"ixTintE8 : Ruitiford's 
Pracoduro ItoH'ltmd'fl Method. Soo 
" Calorimotry, Method of M^ixtures," (7). 
OF UOBY IN QUIESOKNT GAS, BATE 



on ; considered by the method of dimensions. 
Sco " Dynnjnioul Similarity, The Pnnciploa 
of," (28). 

COOLIHU OF IIOVIKH BODY IN A GAS, I.lAI'E OF j 
considered by the method of dimensions. 
See " Dynamical Similarity, The Principles 

of," (30). 

COPPER, ATOMIC HEAT OF, AT Low TBHPEHA- 
TURKS i NoriiHt's values for, tabulated. Soo 
" Caiorimetry, Elcotrioal Methods of," (11), 
Table VI. 

COPPER AND ClJFHOUB OXIDE, EMI8SIVITY 

or i determined by optical pyrometer. Soo 
" Pyrometry, Optical," (ID). 
OOITEH, SOLID AND MOLTEN, EMZSHIVIl'Y 

oi'; determined by optical pyrometer. Soo 
" Pyromotry, Optical," g (21). 
COPPER, Si'EtiiFio HEAT off : 
At Various Toinpoiuturcs j tabulated, with 
tlio Atoinio Heat, Sco " Calorimotry, 
Elccfcmiil MoHiodB of," (10), Table V., 
(12), Tnblo VITI. 
Studied by Harper over the range 15 to 

00 C. 'Scoi'foU (12), 
COHLISS VALVRS FOU STEAM EHGIHKS. Soo 

" Steam Engine, Reciprocating," (6) (i.). 
COIINISII EKQINE. Sco "Steam Engine, 
Itooiprooating," (13). ( 

CoiutitsroNmNd STATICS, VAN DICB WAALS 
TJIEORKJI oi'. Sco " Thonnodynamie-8," 
(00) ; " Thonnal Expansion," (20). 



COUNTER INSTRUMENTS i For 

number of revolutions per unit time. Soo 

"Motors," (1), Vol. III. 
CRANKS, HVOHAULTO. Seo "Hydi'milics," (B9). 
CBANK RFFOIIT DIAOBAMS, Seo " Kinematics 

of Machinory," (8). 
CRITICAL CONSTANTS FOB VAKIOUS FLUIDS, 

IHXPERTMBNTAL VALUES FOB. See " TllOl'llial 
Expansion," (30). 

CRITKJAL POINT, TEMI'KRATUBH AND PRUSS- 
iiiiEj DEFINITIONS OF. Soo " '.l.'hormo- 
dynamics," (37). 

For'Cftloulatioii of Critical Data from Van dor 

Waals' Equation, seo also gg (9) and (GO). 

ORITIOAE, PRKSSORE, KEFIUGEKATION AHOVF. 

THE. Soo " llofrigoration," (2), Fig. 1. 
CRITICAL TEMPEIIATTJRE. Tho tompovaturo to 
which a gas must bo cooled before it ean bo 
liquefied by pressure. If abovo tho critical 
tomporaturo it cannot bo liquefied, fieo 
" Thonnodynainies," gg (37), (42) ; " Liquo- 
faction of Gases." 

CROSBY INDICATOR. See " Pressure, Measure- 
ment of,"(18)(ii.). 

CnufsiiHU GAUGES, Sco " Pressure, Measure- 
ment of," g (14). 
CRYSTALS, NON - ISOTIWPIO, EXPANSION OF. 

Sco " Thonnal Expansion," g (8), (9). 
Thermal Conductivity of. Sco " Hoat, Con- 
duo Lion of," g (0). 

OURBKST Mu't'EBS. See " Hydi'aulios," g (12). 
Calibration of Current Motors. Ibid. (13). 
GUT-OFF. Tho point of tho stroke at which 
tho supply of Htoam to an engine cylinder 
coaacs ia called tho " point of cnit-ofl." Sco 
" Steam Englno, Reciprocating," g (2) (iv.). 
<Jvor,R OF OMUATIONS FOR INTERNAL COM- 
BUSTION ENGINES. Sco " Enginoa, Internal 
Combustion," g (2) j "Engines, Thermo- 
dynamics of Internal Combustion," (2), 
(28) j " Thermodynamics," (8). 
CVOLOIDAI, TJSKTJI. Soo " Kmonmtics of 

Machinery," (fl). 

CYLINDURM, STIIMNOTII OF. Sco " Struoturcs, 
Strength of," (31). 



D 



WORM GKAR T 

MAOHINK, See "Dynamomotora," (0) (i.). 
DAI/TON'S LMV OF PARTIAL PRESSURES 
IN GASEOUS MIXTURES. Sco "Thermo- 1 
dynamics," (02). For proof of Dalton'e 
law on tho molecular theory of gasee soo 
aim g (HO). 

J)AM['KI> IlAHMONItl MOTION. If tllO dl3- 

j)lat!oincnt of a point from its equilibrium 
l>o,si(.i(m is given by an expression of tlio 
form e-i'/am(t + c) tho motion is said 
to bo damped harmonic motion. 
DAY, CLUMKNT, AND SOSMAN, 1008-1012; 
comparison of gaa-tliormomotor with second- 



ary standards of tomporaturo in rango fiOO 
to' 1000. Sco " Tompcratui'i!, 'Realisation 
of Absolute Scale of," (30) (xiv.). 
DBBMSY'S EXI>ERIMENTS ON Fhutn .PRIOTION, 
Tables. Sco " .Friotion," (28). 

'DBFL130TION OF BEAMS. Sco " Stl'UCtlll'ca, 

Strength of," (9). 
DEFLECTION DIAGRAM FOB A FRAME. Sco 

" Structures, Strength of," g (24). 
DEGREE or FREEDOM, DIOPINITION OF. Soo 

" KinomatioR of Machinery," (2). 

DEtmiiE OP IfllEEDOM, EQUI PARTITION OF 

ENEBOY 1 AMONaST BAOiT. Sco " Thormo- 
dynamics," (00). 



DENSITY OF SOLID- DYNAMICAL SIMILARITY, THJS PRINCIPLES OF 



81 



DUNSITY 01-' SOLID, compared with that o 
liquid, for vatioiiH Hiilmtmxcoa, tabulated 
Sco " Thermal lOxpansion," g (;tl), 

J)EVKL01'En AllEA QV A. SfJREW-l'ItOI'ELLEIl i 
the sum of tho netual areas of the blade! 
im;spc<itivo of shapo. See " Ship Resistance 
and Propulsion," (41). 

DBVILLI; AND THOOST, 1857, usod iodine in a 
bull) of porcelain to compare gas-tlionno- 
meters with socomtaiy standards of tern- 
peratnro in tlio range 500 to 1600. Sco 
" To]nporaturc, llcalisation of Absolute 
Scaltt of," (30) (Hi.). 

DrAi'iuiAOM PHjissiriiK GAUGE, Sco " Pressure, 
Measurement of," g (21). 

])IESHL EmiiNM. Soo "Engines, Thermo- 
dynamics) of Internal Combustion," g (31) 
and (/JO) ; " Engines, Internal Conibitstion," 



BIMTBBIOI, Exi'EHifliKNTs OF, in dot omi i nation 
of Latent Heat o Steam. Soo " Latent 
Heat," (1) (ii.). 

DlFFEBENTIAL PULLEY BLOCK WESTON'S 

PuiNciM.B. Seo " Mochanioal Powers," 

(2)(ii.)- 
.DIFFUSION, IKCKEASE OP ENTROPY nun TO, 

Soo " Thermodynamics," ((>2). 
J)iFffu.sioN PuMi-'s. . Roe "Air-pumps," (41). 

Giiedo'a. Soo " Air-pumps," (42). 
BIFFUSIVITY : 

Definition of Thermal. Sco " Meat, Con- 
duction of," SS}(2) (ii.) and (12). 

Thermal, of Soil. Soo ibid, k (12) (i,), 
Table VI. 

Thermal, of Various Substances. Sco 

ibid. Table VII. 
DIMENSIONAL FORMULA OF A PIIYHKJAL 

QUANTITY. An expression showing wiiieh 

of tho fundamental units enter into tho unit 

of tho ([iiaiitity, with thoir (liinonsions, o.g. 

[^^[MJ;! 1 -"], 

.I' 1 being tho unit of foroo, M, L, T those of 
H, length, and time. 

HIONH OF Kl.KdfRKi AND MA(INKTIC) 
ES ; KLIOOTIIOSTATICU. Soo " Dyna- 
mieal Himilarity, Tho Principles of," (3fi). 
lMBiVHIONH, ILojrOdENKlTY OF, IN A PlIY.SKJAL 

.KIJUATION : tho fiindainoHtai prinoiplo that 
all tho torniH in any lunation luiving a 
physiiiial Higiiinoanco must nonoHHarily liftvo 
identical dimonaioiii). Soo " Dynuinioal 
Similarity, Tho Principles of," g (5)'. 
iHii,^ THMOHV ot,- THH KEcmwEn, umul in 
radiation pynunotry to cut dmvn tho ratlin- 
tion by a delinito fraction HO that tho mimo 
gftlvaiuimolitr doilootion in obtained for two 
difforont tomjieraturoH of the radiator, Soo 
" Pyromotry, Total Uadiation," (fi). 

:i>IHtI-AltIi)A HATH) OF A iSliRBW-l'lUll'KLLEll 1H 

tho ratio of tlui fiiiin of the uotua! areas of 
thu hladoH (i.e. tho dwolopml area) to tho 
aim wept (ml hy Win tipn of tlio hladcH, 

VOTi- 1 



Sec "Ship Resistance wild Propulsion," 
S (41) and (14). 

ISl'LACEMENT DIAGRAMS FOB 1'OINTS IN 

A MECHANISM. Sco " Kinematics f 

Machinery," (4), 

IOATOK, Sco " Pressure, 

Measurement of," (IS) (iii.J. 
DOODLE - AOTINO ENDINB. Sen "Steam 

Engine, Reciprocating," (2). 
DiiTFTrjjo TEST OF M.UT,U.S. See "Elastic 

Constants, Determination of," g (;i4), 
Ditoi- TEST OF TYHBS. Sco " Klustio Con- 
stants, Dotonniiiation of," (30), 
DKOI? - VALVES poit STEAM KNOINKS. Sen 

"Steam Engine, Reciprocating," (B) (ii.). 

DuOTtLITY, WOBKSHOl 1 TEST FOIL SCO 

" .Klastio Constanta, Determination, of," 
(14). 
DYNAJIIIOAL EQUATIONS IN TEBHIS ov J)IH- 

l'LAO.EMBNT, FOll ^N El.BCTBKJ SoLIU. Sco 

" Elasticity, Theory of," (7). 
iVNAwiciAt, EQUATIONS IN TERMS OP STIIESS, 
rou AN JJLASTKJ SOLID, See " Elasticity, 
Theory of," (6). 

DYNAMICAL SIMILARITY, T1IK 
.'L10H 01' 



I. ORKKUAL 

(1) GiiNKBAr,. Scientific rcHoareh 
itswlf with tho (lisotivcry and cxpreHHionn of 
laws m oxaut relations butweon physical 
quantities of dillcrent kinds. Jnvolvcd in 
tho cxproasion for tlio magnitude of any eiich 
quantity aro lw uimcopLious Iho natnro or 
kind of unit in teruiH of which it is represented, 
and tho miignitudo or innnhor of times tlio 
unit occurs in tho physical quantity consiilorod. 
Thus, in tho Btnlonienti that tlio earth's 
didinotor is 8000 miles, tlioro is implied tho 
nature of tlio f iindaiiioiitul uiiit (mile) in tennn 
>f whuth tho dinmoler ia mcusurctl, and tlio 
lumber (8000) of thcso units whioli aro present 
n tho physical quantity. H the whole function 
>f aoiontiUu rcseawih conuistcil in a eompari- 
on of qiiftntitic'3 of tho same land then tho 
Icsidorota in tho solocUon of a unit could 
bo easily defined, ami would merely involve 
uoh coimi derations m dofiuilciu'isa, non- 
UBcopliibility to acoular chnnge, and oapiibility 
if nccurato eompurison with tho quantities to 
ii) oxproased in terms of it, Since, however, 
eacaroli in its wider sweop invcfttigaton .and 
xprossca relations botwcen quiuititHss of Hiiah 
ifforont kinds ns forces, toinjiefntui-OH, 
mgnotio moments, otc,, it follows fcfial, for 
implicity and oloarncss, not nioroly tiniBt 
licso units bo aolcotod to natisfy tho above 
equiromimta, bub only snob iniil' must bo 
cooptoil as express all tho (nianUlicR con- 
ornod in tho mmjiiost inaiiiior poysiblo in 
ornia o tho minimum number of indopomiunt 
inifs, 



DYNAMICAL SIMILARITY, THU 1'l.UiNUir.i 



(2) SI-AUK UNITS. l-'or men geometrical 
relations which arc expressions if space trutlm 
involving lengths, areas, ami volumes, it is 
clear that only one independent mill 
required, which, l>ai't *" convomoiiuo ami 
form, may arbitrarily be selected as tho 
unit (if IciiRlli, of area, or of volume. If, 
for example, V, the unit of volume, ho taken 
us the standard dimension, Dion since ilio 
product of three lengths provides a volume), 
tint dimension* of length would bo V", ami 
Hint of area Vl It is obvious that Iho 
dearest and, ti> iw, the simplest expressions 
will bu obtained by chonsing as our standard 
unit it length Jiving dimensions of area 
L a and volume IA 

ij (3) KINKMATH; UNITS. Pacing tu lawn 
involving liinenmtio considerations it. becomes 
at once clear that a new unit iniiHl be intro- 
duced In provide a measure of motion, a 
chari'-e in loiiKtli with timo ; and once mom 
the slmjilout mode of representation is arrived 
at by choosing, not a unit for speed or aceclera- 
tion', and honoo expressing tho fundamental 
idea of timo in a nuiro or less complicated form, 
but by selecting a unit for lime, say T. Speeds 
and accelerations nro then at once seen to 
have thu dimensions L/T mid L/T" respectively. 
(4) DYNAMICAL UNITS. But the two 
units of length and time aro not in thomHclvcs 
sufficient to specify quantities which nrlBO im- 
mediately we enter tho domain of dynamics. 
At the basis uf this aooUon of analysis lies tho 
fundamental idea ol foroo and its represonta- 
tiona in terms of mass und iiucoloration. 
IJeforo a full expression for tho dimenaioiiH of 
dynamical quantities can therefore bo net out, 
cither a now unit of force must ho introduced 
m - terms of which, by NowUm'fi Sooond Law, 
the dimenHion of mnsa could ho expressed, or 
a unit of mass must bo presumed and tho 
dimensions of dynamical quantities derived 
from it. Once more for reasons of simplicity 
wo chooHi) tho latter. Accordingly, writing 
M as tho dimension of the mass unit, the 
following table of quantities and their dimen- 
sional representation may bo drawn up i 



. IJimiitlly. 
Length . 
Timo . . 
MUSH . . 
Liticnv 8|HTtl 
Angulnr spee 
Aooelorntion 
Moment uni 



T 

M 

I/I 1 " 1 

'L'" 1 

LT^ 2 

MI.'L'" 



Kinotiomwrgy . MI. a 'l'~ 
Impuldo . . . ML'.r! 
Work : . . . MI. 2 'J'~ a 
Moment of forai! . ML 2 ! 1 '* 
Moment of Inortiii ML-* 
Density . . . ML' 3 



\ (fi) HflJIOIfKNKl'l'Y 01'' DlMB'NSTONS IN 

rii\'Hi(!Ai, H(}iiATiuN.-- .Since the mathomatica 
formulation of any physical law is a statometv 
of equality or relationship between phynica 
quantities nourasarily of lilte naturii, sincp 
indocd a force cannot bo added to a mass 
but only (o another force, nor a temperature. 



rjunted to an electric charge but only to 
mither temperature, it follows that all the 
erms in any equation having a physical 
ignilicance must necessarily have identical 
limonsioiiB. in the expression for the velocity 
icquircd by a particle m ntciio dropped from 
eat under gravity, for example, 

he dimensions of the left-hand (ride are 
vhile on the right-hand side they arc 

the constant being of course non-dimen- 
sional. This fundamental principle serves not 
ucrely as a cheek on the intelligibility of any 
'ormiila derived either on experimental or 011 
theoretical grounds, but can bo turned to 
nuch greater advantage by providing a priori 
nformation regarding the form which tho 
result of any investigation ought to tako. It 
will become apparent as tho subject develops 
that there exists hero a potent weapon for a 
preliminary analysis of any proposed problem. 
Particularly is thin true in tho realms of 
physios and engineering. 

Tho method that may bo adopted will 
become apparent from a few simple dynamical 
illustrations. Let us assume that the time of 
oscillation of a pendulum in vacua is the. prob- 
lem for analysis, in order to determine how 
the period depends on the length of the HUH- 
pension, the mass of the pendulum boh, and 
the value of gravity. Without a preliminary 
analysis along tho present lines, and failing a 
complete mathematical investigation, it would 
appear at first sight that a complete experi- 
mental study of tho problem would involve a 
threefold series of experiments corresponding 
to variations in longth of suspension, maws 
of bob, and gravity. Consider tho physical 
factors upon which the period might possibly 
bo dependent. They are, mass of bid) w, 
length of suspension I, value of gravity {/, the 
form of attachment possibly, and tho shape 
of tho bob. The last two factors may or may 
not enter, but in any case it is not clear how 
they can bo directly introduced by any single 
convenient symbol. Let us assume then that 
in all the experiments these are invariant, and 
therefore from our a priori knowledge we affirm 

t~f(m, 1, (/), 

where /represents the function which requires 
determination. Lot us suppose this expanded 
in a power series in m, I, and g, so that 
t-'XA.mWfi*, where tho terms A are constants 
independent of i, /, and g and functions only 
of tho shape of the hob. This much, however, 
wo can affirm, that each term in the expression 
must of necessity represent a quantity of tho- 
nature of time, and must therefore have the 
same dimensions as t. 



DYNAMICAL SIMILARITY, THK PRTNOlTLlilS Off 



Kit 



Now tho dimensions of 

and equating UICHO to the dimoiiHioim of ( wo 

find 

r = f) i/-t-" = {) 2"=! 



whcro c is HOUR! unknown constant. A pre- 
liminary analyms of the problem has now re- 
duced tho jioiiosHif'.y for n threefold Hot of 
ox peri men tfj to one experiment, and ono only, 
In determine the value, of c, We have shown 
in fact that thoro arc not in reality three 
variables in, !, and g in the problem, but ono 
single variable (V(f///) which groups together 
a whole system of experiments as essentially 
<if tho Hamo type. What then is the common 
principle tliat runs through tho problems of 
tiio tiiinjs of oscillations of pondnhi of different 
lengths under different values of g, Mint it 
siioiilfl bo possible to group them together J 
What ia tiio phy.sicfil or dynamical significant 
of this grouping ? 

((S) .DYNAMIOAI. SIMILAHITY. In tlio foi'o- 
going analysis wo iniglit oi[Urtt]y welt havo 
tnlton t to ropi'OflOJit tho tinio lalitin for tlio 
Ijcntluhnn to_H\viny out to a .(riven inifrlo n, 
thtiii (=c-V(//i7J, whom c, in now ooiiHtaiil, 
wlion ia iioiiHtant. It follnwH tit oiKio that 
if two putidula of longths I L and ? a , at dilTomnl. 
points on tho ciirth's mirfucsi) such that 
gravity is p, and g s ntHpoctivoly, nro allowed 
to swing, then at all times ^ and ( a suoh thai 

/ I \/(f/^)^^\/((7^/7). tl ll! pcndula will 1m dis- 
placed by efjiml angles. A soriost of photo- 
graphs oil plates of tho saint) HMO taken uf nil 
sutili pondula at any such Horios of correspond- 
ing times will ho identical. 'I'ho goinnotriciil 
tM>nfignratioi\ for all siioJi corresponding times 
aro .similar, fiyatoms in motion whioh can thus 
ho grouped togothor quito gonorally as pass- 
ing through gooniotriotilly idontitsal phasos for 
orjual vuluoH of 11 non-dimoiisional gronpitig of 
ooiTC8j)i)iH]ing quantities in tlm ahovo case 
[or equal values evidently of tvdi/i) aro mid 
to poHscss dynamical similarity. 

,f (7) Ai'i'LitiA'rroN TO PAUTIOLK BVNAMICS. 
V-Considor a furtlior example from pai'tido 
dynamica. A particle of unit mans in pro- 
jected with velocity V in a field of force sndi 
that the acceleration at any point (x, y) is 
A(x, y), what information relative to tho dis- 
tanoo travoi'Hod after any lime in mipplied by 
tho method of dimensions ? For this purpose 
let us write A(x, y) -a , n(.r, y), whero a ia the 
aotnal auceloration nt Homo sjiecinl ])oint, say 
' the point of projection and a(x t y) is tho fune- 
tion giving, as it wore, tho law of distribution 
of acceleration. Under these circumstances 



both A(x, 'if) iind a an; nci'i-loriil iotisi, 
(.i:, ?/) niunt bo of /ero dinionsions. Hnnlriclitii- 
(niwolvna then to a Hoiiea of ^roliloititt I'm 
which this law of distribution ri?]nmnn 1115. 
nhfinged silthough the nuignitudo of llm ti ...... I 

eration at. any point mny vary- -i.e., I ho fund inn 
a rpmains unjifVecdeiJ, but a vriri^rt I'm m 
problem to prohlom we in ny say thai. H, tlu 
(liHtaneo ti-avorsed ivftnr any linm/, is a 1'iinoHtiti 
of V, tho vcliioity uf projetition, a tlm tnt<iitiiri< 
of tho accelei'ation, and / the tinio, i.e, 

S=/(V, , /). 
VVrillng an heforo 

S = SAV"/, 

and crjini.ting fliniciisions, wit find 
(L) l = ic-l-.v. .', :i I-//, 

(T) = ir-h2i/-s, .'. x=l + y t 

.-. S= ilAV'-^ 



Sinco y in quite nrbiti'iiry iind mny linvn any 
value whatsoever 1 while iitill Htitisfyiiiji; llm 
dimoiifiionnl conditioiiH, this iiuplii's that 



v(" 1 } 
\v)' 



whori! l (1 i'c.|in\s[inlH mi nrhilniiy funnlinn. 'i' 
pHrUcular oiw of (luiswlaul, iiin:i>.liM'ii1iiiii aiu 
the direotioti of motion giving tlio wi'll-liio 
forinnla 

K = V/-i-liK 3 

id readily neon to be of this form, for it mny 
written 



(8) NON Bl^rHNHIONAl, V:\lllAltl, I-!H. H 
should bo (ituiitjuliirly rointu'littd Mini Hi" 
])i'obloin HUH votUuiiid ilnelf In Mm (li!lc*niiiiuMf>i 
nf tho relation hotwiwn two min-diiiK^iMliinal 
groups of terms K/V( and at/V, tho ftinc'tli.iiiil 
relation between Iho two dopcnditig ]juri<ly i-n 
tho KC'oniotrusfil cmiuliUoiiH of llio problem ntnl 
in nowiso tin the dyimnnon! piindiiplcn in 
volved. In the simu) way tho eimn uf (In- 
omeilhiting ])(;ndnluin wn reduced to thn clrto 
niination of tlm value of tho single m-n 
dimensional group of ternw, (V(f///) im n im i- 
ninnbor. 

In general, it will lio neon ihat for dytuintintl 
problenifj, at nuiHt three iKjualioiiH c-iin l- 
obtainod from tlm dimoiiHiotis of IIIIIHII, h'li^lli, 
and timo, although there may ho ICMSI if mn 
of these bit ab.sent. In gomirn], lliordfun', I' 
them are n qiiMi titles upcin whieh tlm ln'ti- 
functionut relation depends, the iiidii'c:i "i 
throo of thoHO qunntituw'cian bo OX]IITHMI'I| in 
loriiis of tho otliwf, mid thoro will bo l*'fl > 
illation between n -3 noii-diimmKiiina] ^mni,': 
of tei'iiiH. 

i} ('.)) Al'ITIOA't'tON TO Pr.ANKTAHV Til I, i ill". . 

As a fui'ther oxnmplo oE a slightly clillVii-i.r, 



DYNAMICAL SIMILARITY, THB I'liTNCIPL'RS OV 



natures showing the insight hero provided into 
a problem without actually analysing in detail 
tho dynamical conditions, consider what may 
bo deduced from Newton's Gravitational Law, 
rcgardinc tho periodic times oE planets. 

Tim attractive! forap between two jilnnets of masses 
Wj and ij at distance r apart is, nccording to Now ton, 



Accordingly llie dimensions 1 of k, n gravitationnl 
constant, uro 



If d bo thn major axis nf tho orbit of a planet of mass 
E moving round n central mm S, tlioil T, the periodic 
timttof Hid motion, can depend only on rf, 13, S, and A, 



Ilenao equating lilto dimonsiona 

#4-!)u=0, j/+3 =(), 2M = ] 

r _!l !)= 21- =. -t 



From which Kepler's Third Planetary Law 
follows immediately, that tho square of tho 
periodic time IB proportional to tho cube of 
tho major axis of tho orbit. 

But it is not in tho field of pure dynamics 
that tho method hero developed receives its 
most fruitful applications. In almost all 
branches of physics a preliminary analysis of 
any problom that requires investigation, pro- 
vides an insight into tho main factors which 
arc at work, and thus generally indicates tho 
direction in which tho research should ho 
developed. 

In aerodynamics and acre-engineering, for 
- example, wo are conoornpd with the laws of 
^.jjjr resistance to bodies"?)! various shapes, 



hcaIeiXJtf>dies6MCl\ 
. JiaAiHj*'o"lc, , will cool in a cTTrfciit of 



nir. ' Especially during recent years have 
innumerable problems of this nature arisen 
which, because- of tho complex and intricate 
mathematical expressions for tho physical 
laws involved, have- not yet yielded to 
theoretical analysis, On tho experimental 
Hide, however, a considerable amount of work 
lino liijon carried out, frequently without 
according the results tho full interpretation 
that might Imvo been given them from tho 
present standpoint. It will become evident 
that only by an analysis along tho lines 

' ' write symbolically In 



developed he-re can tho full and most reason- 
able interpretation for any such work he 
obtained. 

\ (10) APPLICATION TO TIIU MOTION nv 
FLUIDS. In dealing with the motion of fluids 
it is iHiofisaaryi in the first instance, to net out 
in detail tins defining properties of that medium, 
f|iiite apart from any theories regarding the 
molecular constitution of the fluid liquid or 
gas. In the selection of nm<h definitive pro- 
perties, then, wo are only eemeorned with 
those that fire culled into action under the 
cireum stances contemplated in tho problem. 
It suffices accordingly to define any fluid as 
dense, viscous, and elastic in tho first instance, 
omitting for tho moment thoHo properties 
that become evident on tho applieation of 
heat. Other properties may makes themselves 
apparent in special eireiimstanoos, whilst even 
sonic of those enumerated above may in other 
circumstances become of littlo consequent. 
If wo are concerned, for example, with the 
dripping of liquid from a tuho, tho elastic 
properties of tho fluid may ho omitted, its 
viscosity may oven play only a minor nart, 
while surface tension enters im an important 
factor since tho problem is clearly affected 
by tho nature of tho conditions at tho surface 
between tho liquid and tho air. 

As far ns all the-so properties are concerned 
it is possible to express their measure, na 
in tho ease of purely dynamical quantities, 
in terms of tho three fundamental units of 
muss, length, and time, from the more defini- 
tion of tho physical properties they are intended 
to represent. 

Viscosity, for example, is introdueod through 
tho coefficient of viscosity i>. defined by : 
^ viscous force per unit area per unit velocity 
gradient ; from which it follows that tho 
dimension!! of p are 

[^] = [Forco]/[Ai'oa] x f Velocity gradient] 



As already indico-tod, density (/>) has dimen- 
sions ML" 3 . Surface tension (K), defined as a 
-ffirco per unit length of a curve, has therefore 
dimensions 

/ " [S] = [Fi)rco]/[Longth;| = MT" a 

y (11) iSmwAOE TENSION. AH an illustra- 
tion of tho uso of those oxprotifttonn, consider 
tho question of determining tho mo. of the 
drops of liquid which fall from a tube of 
given diameter when tho liquid is allowed to 
flow slowly down tho tubo under the influence 
of gravity and capillary force, On general 
physical grounds- on tho basis of our 
oxporionco in fact wo assume- initially that; 
tho mass of tho drops will depend' on tho 
value of tho surface tension between Lho liquid 
and the air, on the density of tho liquid, and 
possibly on its viscosity; ami an far as an 



DYNAMICAL SIMILARITY, THE PRTNCCPLKS OF 



lt n'tial scrutiny nf Hie quoNtion in omH'ornod, 
^Jioso would appear to bo the only properties 
11 f tho (luirl Unit might to enter. On general 
^rounds, moreover, we are amiro Unit for alow 
*n<(tinna viscosity plays a very minor part, 
*<-nd janet) in the- jirtitjent inataneo tho motion 
l! * esscjiil.inlly slow 'since tho fluid is only 
Dripping, viscosity might legitimately bo 
c >Miittod fi'oni tho dismission, but whether or 
lot this is justifiable in of course definitely 
**- question of experiment. Tlio (inly other 
f *Ui tor that would outer then is the size and 
liti[)o of the tube, hot tho diameter ho d, 
I Hit tlio shape cannot bo introduced by any 
cJotinito symbol. 

T.iit iJio muss of each drop M bo ]>ivHiiincd a fimotioii 
<>f H tlio mii'fi\c<! ti'iiHion.jH IKS divinity,;/ gravity, niidrf. 



-''liking tin a typiunl tor in in IJin expansion of this 
f Unotion AWfMj'd", and writing it, (Unions iomdly,, wo 
find 



T -li-nou equaling nowcm of lilm 



t.ypioul ton n in llin:i: 



If mm this wimplo analysis it can oo 
l)o deduced. Unit tho problem under 
imiHt Ijo rogarded as tho determination of tho 
law if variation of tho non-ilimonnioiial group 
with tlio mm - dimoiiHidiial group 

and that einco tho form of tho aj)- 
jiiii-ou'tly arbitrary function <f> can depend on 
nothing but tho shape uf tho tubo, tho curve 
tibtained by plotting MgjSd agiiiiiRt S/gpd" 
\vi\\ lici ehui'iusleristio of that shnpo of tubo 
iitul quite independent of tho actual values 
t>( H, it, (i, etc-. Actually, it has boon found 
f>_y experiment that SI. tho mass of the drops 
IH proportional to d tho diameter of tho tube 
(I'ato'H Law), If wo now therefore examine 
l,lm function (Brf/ffMS/i//^ 3 ), it is clear tliat 
unlcBti tho function </> bo a more constant 
7VI cannot possibly bo proportional to d, and 
tumsequontly on tho basin of ono sot of in- 
-vcHiigatioiiH during whioh d alone JH varied, 
\vliilo Sj p, oto. arc maintained constant, it 

deduced that whon all tho quantities 
- varied 



M-ln!i'o tho ooiiHtanli A may bo dotorniined 
f rum one experiment. 

In tho Hamo way, if the drop of liquid bo 
vibration, tho frequency n will depend on 



ff, f, d, and S ;IH bufore, from which, noting 
that [>i] in T~ l , it can uaaily be shown Lhal 



(12) VlIlRATIOKS OLi' A (JllAVlTATINO LriJDIl) 

OLOHK, A g]o]>e of lif|uid, slush Jis a iikntst 
in a flnnl fitate, iw liold i<igl,her by i(n nwn 
gravity, and in fliifc into a sl.nl a of vibraUoii 
by sonio oxtorntil ilisturbfiniio. Wluifc infuniui- 
lion regarding tho freijimtusy of vilmitiou in 
any of UN uiodcss cmi bo derived by tho 
.Dimensional Method ? 

Tiio friirjnontsy will elom'ly depend on /i tho 
density, d the diunicler of tlio H|iln;n!, and / 
tho gravitational coiifttanl;, asmntiing that 
siii'fiHso tcnsirm and. visisoHity am M'ithiiut 
influence on tho C[uestioii. Accordingly 

n=f(p, d, Jc)=^A.p a (l s k tl . 

Tho diineiiHioiidl oxprcssioiis for cacli of tho 
(piaiititios d and k tu-o ktinwn and have fllremly 
betiii used. Jnsortintj thcuo it followH at OHCO 
Unit, x^-z--=^\ y = f>. 

Henoo . n<-'- \'(jik), 
and it a])|)(iai'.n that tlio frc<|iion<yy IB in- 
ddpcndont of tlio tliiimctor of 1,Im spluirB and 
proportional to the wjimro root nf llio (Uinniiy. 

(13) VuMKirTv tit 1 WAVKH. ISy iv nimibir 
]]ro(!enrt iif roiinoniiiK it in t-iiHy to cutabliHli 
tho fornndiio foi 1 tho wuvo vtslocity '" Lh OUHL- 
of Imavy gravity wa-ves in deep wu, v^<---(i\ 
whdi'o \ in tlio wavo-lcnglli, and y 3 v:,S/\p for 
Hiniill surfju!(!-toimicin WHVOH. 

A olour inyight into tlio i)i'inri]ili-a of 
Similitude that lio at tho banin of HUH method 
is boot ft Horded by n gunural l-rciitinont of tho 
inotiiHi of a vJHHuus lluiil, (.somilaUiiH nuiny 
ajipnrontly divor.se jihondinona, ami luyinj; 
thoni oloai 1 a^ natund (!<}iiat!<piomi<!.i of tho 
oporatiiin of tho gtmornl pnnoipln nf Dyniuntttal 
Similarity. 

g (M) jroTiDN ov A BODY IN A Visoous 
Fr.uin. Lot it bo mipnusud Uia-t a holly or 
system of budics of givoii goometricnl sl]fi]io, 
and size HpccificU by tho length I of some 
portion of tho system, is moving with velocity 
V in a fluid of dcmwity /) and kinoiuatio viHcowiLy 
v(~nlp) t and for tho moment it will ho 
presumed that tlio fluid IH inelastic, AH u 
matter of actual ox])<irim<mt it in found that 
not until the velocity apjmmohuH that of 
sound waves in tho inodium do its cltutlio 
proportion make tlioniaolvoH a])])fin;nt, ',1'lnin 
tho volooity v at HODIO |)oint o lUo fluid 
goomotrioally fixed with rcteronco to tho bmly 
may quite generally bo written aa 



while tlio slono of tho stream lino at that 
point IB 



Applying tho jirinuiiilo of ll'omogoni'.ily nf 
Diinonnions and romoinlioriiig that 0, the 



'DYNAMICAL RDttLATlITY, THE PRINCIPLES OF 



slnjH'!, in of y.om dimensions boing a mor 
number, it is found, (hat 



Tlio switond tKjimliou indicate that the shape- 
uf. the- fit-ream line-Blind the direction^ motioi 
at any time de-pond only mi tho valno of UK 
iinn-diiiMmsbnal group Vljv, niul not on tin 
.separate constituents of that group. The 
magnitude of tin! velocity likewise- depends 
on Vljv and on V alunts. Wo so in faet that 
provided a ay.Hlom of lindios are all geometric- 
iilly similar, their sixes being different, the 
Hystrsma of Hlreiun lines generated are likewise 
nimilnr, provided \llv Is maintained constant 
throughout tlio system. 

Jj(in) ItHYNOLDs' NiJMiii'iit. As a muttor 
of autiial experiment Keyimlds, 1 by a ImJlinnt 
serins i'f investigations, demonstrated that 
tho whole pnxsess which takes place dining 
the motion of a fluid docs not depend iikmo 
on any of fho single quantities V, I, t>, but 
im tlio group ; moreover that for any given 
problem in his case tho How of Unit! through 
eiroulnr pijios V//c ia a critical variaUo, 
whinh when it attains a curtain value oorro- 
HlKHicU to a inoro or loss rajiid cliango from 
otio state uf flow to another, from tho steady 
80-ciUloil Htrcani-liiio flow to tho sinuous and 
turbulent stale) of eddy formation. Lot us 
BiipnoKO llioti that eddying has originated, 
limb is to say that this fluid on UH pasnago past 
Hio obstacle fin-ins in (ho neigJibfiurhood of tho 
Hides o tbo latter a sysloni of oildicH whioh 
aro shod periodicully. 

(]fi) FiujyOKxcv OF Kiniy FOHMAT.ION, 

Lot n bo tho EfOfiuoncy of those oddios, then 

dourly it can only he a function of V, I, v t and 

flpm-fc from tho gounu'trical shayo of Uio 



Hoinoniboi'tng that tho diinonsion of -n, in 'I.'- 1 
and applying tho inuthml of this article, ivo 
easily find 



indiisaling'onco more that if Vljv in maintiiinod 
(!0]inlant for a stories of similarly ahaped bodies, 
for such, ft system 

.. V V 2 P 



Ifonoo fur a given raluo cif Vl/r, and a given 
fluid! no thut v is al.su constant, the frcqucmoy 
ia (mtportioiml tu tho flf[iiaro of .the volooity 
or invorsoty an tho square of llm sin-o. 

(17) DrNABIIGAI, SlJIILAUlTY IK TiriJ 

MO-WON or A Viscous FrjfiD. What this 
J Mai, a ; ra. clxxlv. 1)35 ; Ooltc.cied Works, \\. 51. 



implies may bo sumnmi't.sed by HiiyJim j ft' 1 *' 
if a .Horios of bodies all of tlio same gciiiini 1 .(. r jii.^.i' t ' 
shape be moving in a. system of IhiiilH, VJMI^ ) M i 4 J |T ** 

I'D "ai U'if-'l vdoeiliisfl V,, V Mt 1 *' 1 

provided V//c is mainlained constant, ulnpl-'*" 
graphs of fhe flow pattern taken on moi n ,,,.(,* "" 
graph films of the aamo siv-o will all bo idc>n (,i'- J1 ' 
as far as the eoiiHORiitive geometrical ioji(iin'i i'Ji- 
tiojis of (ho stream lines anel eddying 
are coneorniid. 

Tho rates at which tlio proiiosHOh 

themsolvcH will, however, bu dilTnront, ., 

fact delcrniiiiod by the cxpnwHioiiH for (,f u> ' 
rpiency 7i, hut clearly if tin; pholo^niili H 1 
compared at con-espimditig limes an Indi-mt.i-t^ 
above, the pictures will be identical. \V ( , m 
in fact that tho esondition, V//i' --ennui .... i 
inviiivos for geometrical sitiiilarity ut 
niics, [)hysi(;id similarity in tho mofit.tm. 

Tins idea has been sei/.ed upon and UHIN 1 t 
great advantage in aerodynamical ami n^v** ' 
(iriiliitoctural analysis, for, nn will ho iimiii>ili- 
atclysoen, it provielcs tho banis for tho unit I vnin 
of full-scale problems in aeroplane, iui.Hlii]i, 
and naval cimstruotion, by means of I.<!H(.H *ii 
models. 

(18) lllJI.ATIQN .tiETWJ'JUM 'KXCIIKTM I.JM'I'H 
ON MoiUJL AND ON lAir,], tSoAI.H. - Ki 14 1 1 1 

analysis, in general, centres Until f routii) t-Ii<> 
qucslitm of how, from moasnromonlH ttf i.lm 
fortioa originated during the motion (if tint 
moilol, to predict tho cnmsspi Hiding riiriu*.^ 
that will ho called into play during tho un>lic mi 
of a fii|[-ncalo nmehitio or part. 

Tho details of this will bo j^iven in iui()(.]i4*r 
section ( " Aocomuities Sealo-olTuct"), 1 hub fcit 1 
tho purposes of the present arliolo wo uni^y 
iiolo tho main principles at work. If .it, -* ; 
resistance of a body of dimension / in i I.M 
million through fluid of deiinity /land vwfiimii.v *' 
with volooity V, u-enmysay that 11 --;/(/, V t //j-) 
iml applying again tho motluid of thn ]intHi i rii t- 
we easily determine U in tho form 



(1!)) NON - UIMBKSIONAI. MlWIHTA-NHi: ( '(>. 

imaoiHNT. Stating tho law <if mtmhunicj in 
honinnnor Unit has been followerl in pruvi> JIJH, 
analysis as a relation between tu-o IHHI- 
linionaional groups of terms 



ndicating that tho question of the fiir- 
isting a liody in its motion tli rough a v 
luid is most projicrly roproaontcd n,s n 
howing.tho vaiialion of tho " rcHistauci-i <icj. 
ftioiont" (non-dimonakmal) B//iV' J ( a u c*rM- 
lato, against Reynolds' rum - dimoiiBi< >i i ill 
lumbar Vl/v, as a base. 

(20) CirAllAOTRRISTrO CUBVK. KlUlH It 

urvo will bo characteristic) ot that Hhupu < f 
1 Sco Vol. IV. 



DYNAMICAL RFMILARlTy, THK TRmfJTPLKR OF 



87 



body, lint will bo aliHuluhOy ind^muddnt of 

till! "HCitlll!" Of 1ll(t lirnUloil! lltlll Of Ult! COIl- 

HisiL'iit wot t.f units in IITIIIH of whiiiJi the 
various faoloiu am oxprrastnL If thoi'.'furo 
by oxporinwnfc on a inodrl of an aiiuhip 
'anmplanc, (n- any portion of it, values of Hit 
resistant*! (loollhiidnt mil be obtained for a 
snllidimfly widu rango of tho sin^lo varinMc 
V//i> tlio atuno I'oHiHtiiiKse.) dorivative will bo 
valid fou tlio full wiulo a,t (ho aamo value o 
V7/i>. 1 11 not iiiil pmutioo it is oxlrompl 
diflieult, oxwpt in ram cawa, to attain i 
HufJidontly witlo ruugo of this quantity, am 
' methods of oxtt'iiimlation supported by full 
Hoalo oxpm'imoiits have to bo renortod to".* 

1'iH'tiijiitioly, extrapolation in groatly simpli- 
fied in praislkio by tlio fnot that foi- iiioroauiiij, 
values of Vl/f, the nssmUnco (onds to imm:u 
steadily a<i tlio mpmro <ip UK, spiscd, HO that 
H/,jV 2 / a , and eoiineituoiitly /(W/i') ( toiula to 
become coiiHtnnt. 

_ (21) Jf'oiuihia nuiuNd A(;c].;r,h:uATHD 
MOTION, lii HID abovo dininiHHioti wo luivo 
niiiroly (i(inHulrod tlio q_m!Hl.ioii of tlio forties 
cnlled into ]jlay when tlio body \n m stcjuiy 
niotiiin. Onn \vo (liirivo frotn fimt |mnoi|)l('n 
any infornialirm ri^'ardiiig tlio iiiilnro of l,|i 
rcsistiuico wlion tlio body, moving nndor nil 
ncooli) ration a, my, IIIIHS-HIH tliroii^li tlio vi;lo- 
city v, without our having nxsmirso to tlio 
emu plicated iimtluirnatkiH of fluid Tiiotion ? 
Eni|)loymy tlio HUNK! HymliolH us pruvioiiHly, 
but writing v us tlio vulddiLy not of uteiwiv 
motion but of tho body at Llui jjistaiit undcsr 
connidorttlion, and a its iiiiuc-IoratHtu at tliat 
inoniotit, tliou following Iho IU-OOKHM ulroady 
adopted wo obtain as tlio cxproasion for tli'u 
rcsistanoo 



where in addition to tho noii-dimunmoiml 
group Vl/ti alroady obtaiiuid, tlioro in now 
introdiKsiid tho ox|)i-oHHion //i; a on wliitih tho 
additional nwinlainst) do]iiiinln, not, ho ib noted, 
on tho aooolonilion ahum, lmt on tlio vaiiatiun 
of thin group. 

8(23) VIRTUAL HAHH. Tu (ltormino inoi'ti 
' 



i, 

lot l.l--mii,sl;an(!o for wti'aily motion at volocity 
)', and 1! -|- H\i tlio rosiHiiHKSd for an auuolomtioii 
term itl/u* mimll compared to unity, tliou 



and 



f "" 



that tho iiddilieinal fnivn 
liy tlin iu!(;<)]nil.(id ni'ttinn i^ i'i|iuil f ., 
inquired to givo n IHIIHSI of fluid I'Pf^rl],'^}} 
tho (icisiiJonifidj) <t of tlio Imdy. lint ,)/ :t in 
propurtional In Lho mass nf "tho dinplnord 
lluid, and coimo(]iir.']itly it followH that for a 
given viiluo uf nljv, this oJToi't nf mu'olocjiting 
tho iiiotiun \ to givo rjuo to an niipjirmit, 
itujrouso in ninsH pro|)iii'(.iinial to tho 11111.1.1 of 
tlio fluid diHnliKiisd. 

mits nf thin HiMiulhid " virtiml 
aro of ini]iortanoo in tho .stability nf 
lurMhipH wlmro thn ina.HH of fluid dittphuird in 
tlio siuiio as tho (olid woiglit of Mm wlujj, and 
wlmro (ioiifii'<|ii(!ii|.|y UKI " virtual IIIHHS " may 
anqiiiro a iioiiidiloralilo tnajjiiitinh-. It muy 
bo ninuu-ktid that for iiivi'Htig!i(.ion of 
nutiiro tho roHiillH would natunilly ho 
showing tho variation of tho iiim'-dtnioiMionul 
waititmiM, nnoiliuii-nt R/pvW eithmi 1 wit It rl/i> 
for various values of iitft^ 01- (siinvcirwly, 
and for a ucmipltilu iiivisstigadiiii tho full 
'o to infinity, of nt/n s must lin 

XJ'KIUMUNTAI, Dl-STKUMIXATION (U-' 

MAH.S. ifur hmgitiidinal ncicnlitrn. 
tiniiH Hiioh ti.xnorinu'iilB luivo licru onocivHHfiilly 
tj(judii(!ti!(]. a A hody dt'o|i]H!(l fmm ivnt nnil 
alhiwod fo fall in a, fluid (ill it evaolii-H i( M 
liniiling vclucity, given at Urn ooJiiiiitMiiininotil. 
of Urn full t>: i) and if. nnd / ftiiltfi HO thut 
thooi-olkially //^->r.: w hil<>, wlion tlio limiting 
velocity in rmiuhrd a -.-(}, nnil latul v aro linifo 
MO thitf; a pliutu^ruphio nl,udy of (Im iihuugn in 
motion then provide HiilTuiont data la nloU'r. 
tiio virtual num. 

and uarcful av|ioriiiHints luwti 
(londuotod to tost Hm lusonmuy uf tlm 
doduolion that for iinii-mjiiuliti'iiliKl liiolion 

C a vinooim fluid tlm Htatu o( itffiui-ri (Jqiondn 
moroly mi tho vnliio of vf.fi; .H(^ynuldH, a an 
ulroiuly indiwittid, Hliowml lioyond 'doubt Unit 

r tho llnw of a liquid in a titFw tlic; JUIHH- 
igo fnmi steady to HiniuiHH od<lying motinji 
JiiciurH jiun'o or \<m Hharjtly at a dcliniLo vahm 
>f thin niim])i)i'. Ktantim and I'unimH,* fol- 
owing up tliOHo oxjiuriiiioiiLs, vnnlii-d flmf 
'in* air a fiiniilar result Md. Miimo Ihoit 
unnoroim iirodiijtioHH fmm tnodol rcHidiH in 
lonmiiHtionl and inarino invcHtigatiiniH In full 
ualo luivo (Hnnplotcly jiiHfillwl (ho d<Mlun(ionn. 
)n Iho olh(tr limid, it m | ( iar that the oinnint- 
tiMHjiwi of Hit) problem nnitit ho mmh an will 
lot involve tlio origination of |in>purtk'H .f 
ho niodiuin prrwinmHl nmi-oxiHioiit-. 

V. III 



. 

-MfB, for oxamplo, wtt a 
hn iiintltin of a hody at npcoiln 
lio voliwilyol tioiiml, wUhutfflio mil-lit oxjiru 
hat not nioroly would onoi'jjty linhwt during (h 



J '" f 



J Tttim. ll.H,, /tic. rii. 
1 Ibid, A., iTXlv. I!)1)-'J 



DYNAMICAL KFMLLAlU'rY, THE PRINCIPLES 01? 



motion in overcoming viscous forces, but a.lfui 
in the production of waves; that ia to Kay, 
we must now regard the medium as being 
both vifidoiia and compress! vo, Now the 
velocity nf Bound in a medium of elasticity 
.K, density f>, mid vittcdsity v, is given generally 

antl of|_i luting like dimensions wo easily iind 

"v-A "/I 

..V-.A.. s /(- 

'I'o find tho modified expression for tho resist- 
unco in this case wo write 

and following tlio normal procedure v/o dorivo 



li 

V 

where Vis tlio velocity of wound in tlio medium, 
indicating Unit lor a given value of vljv, tlio 
rcsiHtimce enolficicnt depmula solely on tlio 
ratio of the velocity of tho projectile to the 
volooity of Hmmd. 

jj (Sit) ErifJttJT OF HOTATION: PllOl'EIJ.UK; 

Sui'iu..- If in mldition tlio body possesses a 
spin li duo ti> rifling, there would bo present a 



li _ fvl v flj\ 

' pv-i-^'^p* V' v )' 



Two poi]tts nf ini])(n'ta nee may bo noted. In 
tlio firnt pluco for BiH'h liigli Rjiccdw aa would 
utuiso tho ulaaticity of tho medium to play an 
important jnirt, tlio value of vlji> would in 
gonorat Ijo BO largo aa already to bo woll above 
tho rinifjo for so-uiilled Kcsulo variiition for tho 
vJsuoiiH iorcc.H ; that is to my, further Jncreitso 
in vjduc of tho tunn vljy would liavo no nitirked 
iitfluenco 011 tlio vidno of tlio nisiwlaiu.')) co- 
In tlio second jilnee, nrohloniH of 
iinjKirLiinco involving tlio rotation 
of moving bodies diviflu IheniHolvoa tinder two 
heads j thtiso in which tlio term ii//u iH of 
primo imiH irtivniio us in tho enso of the jiro- 
pollor ; nucl. those in whiuh tlio apin hns no 
aiqu'ocialiJo offeot on tho rcHiatuiusu aa in tho 
onso of bodios ayininoineal about tlio axis of 
rotation BhollK, hullots, etc. In tho latter 
onso tUo rotation, exists only for purposns of 
stability niu5 directivity, and playa no incasin 1 - 
al>Io part in niToctmg tho rcsmtanco. 1 Ho- 
Btriuting onrselvca to tho second, purt, espon-- 
monifi on n1liti(fs cfindnotcd prior to and 
during tho wfir (11U4-1S) liavo succeeded in 
liroriiliiiK n more or ]?w eonipleto ropresonta- 
tiou of tho forces on a projectile (fthell) for 

1 A dlsciiKalon o( HID iinrfonniiiici} of proiidlcm ail 
ft fini(!Lloi of tlio mm-iHmi)ii3loriiil groiii) (tf/i 1 will 
bo Coiiiulniulor " I'topcllera." 



speeds varying up to and well over 2000 fi-t't 
JIEJI- seoimd. It ia found that ]>li)tting K//"""'" 
thti I'caisfcanco coeflioient, against vj\', tlio <!iir'%'<> 
remains iiraetioally af.rjiight and hori/.oiiitjil 
until a Kpoetl iippromihing tluit of wninil ^ 
attained, when it risea steeply and turn in;-' 
at tho critical H|iccd diniiTiiHhus slowly. ' ' r 
appoara then tliat in tho roaion of f.lii^ cuil^'iil 
spuctl pi'O]iortics of tho modiinn enter whitsli "|' 
to that point play no |irt. Tho most luil.iirfil 
inm-dimenHioiia.1 base for ro|n'osonl;ati(in tln-n 
changes from vtjv at low ppee-da to c/V alv bi^li 



It may bo mentioned in passing that in Mm 
ease of tho Horow motion of a body not HVIM- 
mcstrical about tho axis of rotation, mush HH iv 
jjronoUor for oxamplo, our discussion HO fjii" 
implies that at HpeodH at which the vistsnuii 
iiuiilo eiTeot duo to tho presence of tins 1'f/i' 
term is no longer of importance as a variant, 
tho term Ji//w will become tho principal nnJi- 
dimcn.Hioiial base of variation until tho Njwc'Usi 
developed approach tho velocity of HOUIH), 
wbon tho now factor /V will begin to oxoroiHn 
an iiicronsing influence. Tho anticipation Unit 
at Hiieh high H]>eeds a critical ntnto will wisi in 
is fully borne out by experiment, 

!By tho method of thin chapter it is (svitUMit 
(hat tho expression for tho pitch of tho uotn 
prodiiecd by tho rotation of a propeller ilk 
normal Hpoeda will be given by 



whilo for cxeoHsivo speeds 



!For aiieh an instrument as an Aoolian ]mf|> 
if d~ diuinetoi 1 of wires, tho pitch of tlio imf.u in 



Actually Strouhul lias found oxporhmmtiilly 
nt.i(vlit) indicating that tho function is a nn*r* 
constant, It Blionkl be romarked tin it IL 
shnilnr expression ivas found for tho porinc! 
of tho eddies produced by tlio passage of Mm 
wind pnat the wires, thus miggeHtin^ thti 

H'.tion betwiten tho two jihonoinoiia, 
(2(1) J)]-JIIUOTION OF SAVART'S LAW. An 
intercHting illuatration of tho power poHstsufMstl 
liy tlio dimciiHional method of reducing experi- 
mental investigation to tho necessary minimum 
is afforded by tho investigations of Savart E on 
tho notes soundod by simitar vosHola contain- 
ing air. Tho law proposed by him aft*a* an 
oltibmuto scries of experiments over oxtroimi 
limits; many notes, and mimoroun ahaposi (tf 
rcffonating boxes, was that tho numlW of 
vibrations per second, or pitch of tho ro 

Awiales tie Chitnie, ]?nrjH, 18!i5, xxlx. 



DYNAMIOA'L SIMILARITY, VKK 



SI) 



mto, is invorstily proportional to tin; linrmr 
limeiirtioiiH of llio vfissol. HIM o.xpuriincnts 

Iiclllllnil U'Sbi Oil ])<Xl)H in tllO ftllllpO of OllllC'fl, 

tiibusi, Clinical pipun, eto., nil of 
wore Hot rc-sonuting in diffomnt ways. 
I'liifi result, to establish which reijuiroil tuidi an 
ilaborato Kuril's of experiments, can bo neon to 
ollnw at mico from iliimmsiimal oonsidoiutioiiH, 
or, if 11 I)LI tins number of vibrations par 
eoouil, K ami /> bis HID ulnstiisily and clonHity 
if MID medium and I a liniHir dinionmon of Urn 
ox, then "/(/, I'j, /)) anil rurnenihoriny l.hut 
wJ = T-' 1 | i IOJ = ML- 1 T- a nmljpl -iML- ;i , it 
i easily soon that w.cel//\'(l | Vp) whoro the 
onstant. of proportionality depends punsly 
'ii (.ho shape of tlio vessel : Savart's Lnw 
ullowH nt OIKJO. 

(27) T HH run ATI; HH. In Ui fnrcf-foiii}-; <l>- 
UHHirm it luiii boon pi'isHiiniiiil tbut tho t(.'iii])i.'rn- 
iiro of tlio iiicfliiini remains oonstiiut, or ut 
ny rn to it duos tint l)ring into jmimmcm'o 
ny now iini[Jiii'ty of tlto inwliiiin. It In nmv 
iroposoil to rtiinovo tlii.4 ri'ntrintioii. 'I'lio 
onoo|ition of t(ini|ioratiiro is nt' an I'swi'iitially 
iiToronfc natnro from any nf tliowo wo Imvo 
Intaily ilisunHyistl. 'I'lin Hiuilo uf IciniKinituro 
i ni!lc(;t(!(l to jini viilii HOIHO hasiH for tint 
icaanroiiKint (it "hotnc.Hs" nf n lioily, 
Liivinj,' (it nur diapiiHiil HliindanJH i>f IIIII^H, 
sngth, iind timo only, it iH]iuiiiif('aLlyim|>i>HHil>li 
y means of tliom to ilotunnino or n^midi'iiii a 
!in])i'ratuni ; for thin |)iir]ioHo mnnii otlii'r 
ropL'i'ty of iniiltoi 1 UK diVotstisd tiy hcut niunt 
o Holcotnd to Hui'vo IIH ti Hlimda.rd of ini'iiHurii" 
milt. Aoisoriliiiffly, it lioiniiiii'.H noccitiiary ut 
m Htu^o (.0 intmdiu'i! a mnv unit I) uf 
(ni|)oraUiro, and in tornis of Him and Hut 
nitn already adopfisd ill Hhoiild bo [in-Hmlilo to 
ritu do\vn M'itii in|)anitivo onwo Llio diinwn- 
onal oxprosfmniH for tlio (|_nanlilit i s tluit; nmv 
.'[HO. 

In dealing with tlio comlmiUon and (inn- 
xjtion of lii-'alv lliwi'ti iiro tiro tjooniuionls, 
iaraot(!L'inti<i ol any purtioiiiar Hiiliatanco, 
IIOHO cli monmoiiH will bo niijuirod j tlmy arn, 

quantity nifiimuring llio aiuount of liuat 
nit niiiHt lio H'vun to nuH unit volininj cif 
10 medium through unit dojn'oo of Umiporii- 
iro, anil a quantity inci muring tlio hunt tmns- 
rrofl aoroas u Hcution of unit doptli am! unit 
ca in unit timo for unit dilToronou in 
mpwntiuu Tlioso qiuintitioH art) of crmi'ao 
Hpisutivfily the spuoilio hont (<;) nail the 
.ormal tiondiiiitivity (la) of tlio nu'ilinni. 
Ex|ir(;Haiii{f liont onlimly in tcmns of oiiorpy 
lita whore it DCOIH-H, it Mum follown that 



connection with iniiny problems of conveo- 
n, tlio effeut of tlio oxpaimiou of thu uir 



uncliir llio hiHiHiniiu of the; InintniJ HHifuci'C nmv 
attiiin miiiH) conHklonihlc impnrUni-i! in I hi' 
f.i'n.iiBrinnKion of tlio lii'iil, mid as n iKintH'ijiH'iirn 
i.lii! quantity d iw inti'uduix!*!, n:[H'i'W!iiiin^ lln- 
wliiuijfo in dcnwity jici 1 unit cJmuyi 1 in Icin- 
])i'i'fituro, or -j 



ij (SiH) KATK OF (,'CHII.INH OK liunv UN 
ivNT <"iAs. J\H tin illuftl ration nf lb,> 
uUlity of I.IK) itiiitliod <if diincnsioiih in llio 

diHCUHHUUl t){ JirohlllHL.4 of lilinlill^, Cnnnidl'l' 
tlio mil) of IOHH nf lictit /( of iv lindy of fjjvcii 
Hliupi!, of ni/i) / uf OIK; piiil, in it <|iii<'NiTiil. 
iLtiiHispluM'o nf deimity /> and IviiuMinil in 
viHisoHity r-, 'if /, anil < Inwi! (lio inciniinjiri 
jHvvidiiHly jiKsuiliud to l.licni and O 3io i]w 
f.<!iii|iornl.iim tliflonsmn; inuinlaiiKid Imtwfcn liin 
liudy and tint giiM at a k'l'rut ilialainio, at wilted 
tho liitlcr iw nndiNliii'ljcd by tins prc.wtn:^ of 
tin) body, it will ho jimlilinMo tn wiilo 

*=/(/, k,c, />, I-, 0), 

n.HrtiimiiiH thai, in tliiM caw* Mm* (.'lifiiijjrii in 
doiutity (lil.l! ^'iiipi-nitiii'i) n re tint HiilJii^iriit. l.u 
all'i'ist thn ijurslinu. Tlio niniliiii-nl iuiitt in(u>. 
dimril if (]||H (iriiiilitiiin in vinlnlnl will Im 
ii|)piiri(iit, anil iidjimtiiu'til. caily nuidc, 

liniif;iiiiii[{ tint fmiolion / c\[i!iHtH''l un in |.iT\iuni 
illiint raliiuiii in tin; Win 



(if Ii, tllO lutl' (if lll'.'ll. !(1!L!1, DTI 1 (llUMII ll( 

(\-v-a\v ( 



.'. .1!' '! -'.'.It, If -t 'iZlt l', 

a"--j-~;iM-j-u, iu=-.il -11, 
Thin providoH a Lypiisal U.'nn in Mm i-\ 



and ticniHWjuontly HIIICO , v, and Mm 
(Miolliijiont of ciush (onn may an fur nu can 
lumi bo dnliM'iiihird liavo any VH|LI 
amwor, it is Ln hu (Kinuludcd that 



Whether nr not all Llio i|iinn(itii'H whitih 
linen iiHHiuiKid of irnpoj'LiiiH'd En Mio ilcdcr- 
mimititm of k uotually t\u enlor in a (iin-olinn 
ta bo divided only by L>xi>urinu)iiL, lo which 
wo nti all roturii shortly, 

(20) Nl)N - IHMEMHJONAL VAlll A JJT.4.-- l''ul' 

tlio inomont it nan bo omiuliidiui tluit Mui 



DYNAMTGAL SfMILAmTV, TIT.R PRINCIPLES OF 



problem i)f I'ftto of cooling in this itistaiu;c 
reduces itsHf tii a consi(lorii.Udii of tho varia- 
tion not nf /;. uloiu;, but of tlm iioa-diimiu.siorial 
group /r/JiO with the mm-tlimonsidiirtl variants 
(il^(l~c?(-) and (('//.'. If we arc dealing \vifcli tho 
ruto of ctmting in gas us then practically c^/i-, 
tho ratio of tho cmissivitius for niomciiitinn 
ami fur liont, is u constant for all gn.sos, and 
consequently this term may bu omitted from 
tho function /. 

A considerable number of experimental 
mvoHtijrfttinnsj IULVO boon conducted on. this 
problem and in nil cases it bus boon found 
that the I'tiLis of heat loss varies directly as 
tho tompora.tni'0 clifforfliiuo 0. In en'uot Lhia 
implies that ft/0 it) im lap out tent of O ancL Unit 
iionsicipienlly /(h-pfl-t-M)) ulmvo in a 
Il'otieo 



indicating thai Mio rule nf cooling in pro- 
portional tn Mid SUKO of fclm liody mill tn fcho 
eondnolivity. Tho conllkiiont a dopoiulN uf 
oourao un tJirs Hlmjio of tlio cooling hudy. 

Tf, hmvcvm-, it is illegitiinato to UHSIHIKJ that 
tho DxjiaTwiou of tho {fia duo to heating is 
ncglij^iblo 11 N a fan tor in. boat trftiiainisHion, but 
thut Iho oxpandod portions hocoiuiiig themby 
rolutivoly JigJiLor will toml to stream upwards, 
anil us it, conHoiiuonco tho heavier purliotis 
downwards, a now term inU'odiiciiirr the 0(11111^0 
in weight . cif unit volume por unifc olmngo 
in tomnoraturo niuot bo considorcd. Suoli a 
factor in of OOLII-HO fl(3/)/30) (?r gS. 
lloiico gonorally 

*=/(*, k, c, p, i', 0, i/5), 
and following tho lines of llio provioim argil- 



jiddnoed in tho fnnnor -case, 
Kii/liflkmtiy uppraxiiniito for nil 



For fclm 
thti film] 
pmutictil 



pi'ovitlod fcho problem is restricted In heat 
fcrnnamfosion in gnaca. 'I'lio form of tho 
fiinolioii x> (Uipondiiig aa it tloiss on tho wliapc 
of the body under consideration, will now 
bo completely datornneiod grtiphioally from 
'a Hinglo net of oxporimoiits for whiah tho imn- 
(liinonsionul gmiiii IgS/o is allowed to vary 
ovor n ratine, for caoli point of wlitoli tho non- 
diinonsionn] tonn hflkQ \s measured. Tho 
rwmlUng oiirvo obtained, invnriahlo for all 
sytoiH of unita, will thon ho chnrnctoi-iHtic 
of (Jinan special lioinulancs. 

(HO) HATH OF COOHNO or A MOVING ]JODY 

IN A OAH, Problems of great praotioal iniporl:- 

(incc tvviHo in ooniifiotion ivifcli tho rato of liuat 

1 fcranamiaaion from biidit-H in motion in tho air, 

na in tho caso of rndiatora nml air-cooled 



cnjfiiws. In these jiroJdoms tho mto nf i t .n'' 
t-raiifjniirtsir)n will actually (ki])i>m) mi th<> (.,.,, ,|H- 
latinnal velocity V in addition to tlio cjimn (,i i it*- 14 
nli'tjiuly I'liiiiiicraldil ntiovL 1 . Tho iiitn><[,, c , j j,-i> 
of tliift oxtra ayinbrd, as unii ousily In., vnri f ii' 1 ' 
by an application of UIR (HiiuiiiKiorm] inc!lK|][f 
givti-s riao In tho " fhiitl inotinn" toi-ni \''//'' 
in the functional expression. If uudi-i- tJu'^t* 
tiirBiunstancoa it can lugitiimxloly be ]>]'(>nn n n'<l 
thut tho icnn brought in by tho nitn of ulni.ii^* 
of density would not materially alTee-l- |,li,, t .^ t |.i 
of boat transmission, an asuumplion thuf, ^'iH 
bo tsxamined shortlj', then, for reasons alr<>n.( J V 
sot forth, 



i'fk is constant for n gas, 
'< - , f Vl \ ' 



'-'I' 



V / 



H'il) Kxi'l'lHIMUNTAL DBTMItMrNATION" Ol'" 

UNKNOWN KIINCTION. [n the caso of UcMtt; 
loss from long circular wires past which nit' 
ifi streaming with velocity V, it has boon found l 
that ft varies approximately as V^. If ft if 
tho momenfc this ho accepted as onrreet, it in 
yosiiiblo immediately to determine tfm form 
of tho function, for the only expression for V* 
sueli ns wilt make /iyi in A \'(Vlfi'\. If 
the wire, moreover, is of dhunetor u, it in cju ilo 
legitimate to substitute for I in this ttsrru in 
order that when tho wire in of inlinito ]anu;1 I 1 " 
them may result n. finite heat hiss per urii*> 
length. It follows, thercforo, on tho for(.'f*c>iii|Jt 
assumption that 

V\ ,, /7 V S 
'.' ) " " V ^ k ) ' 
tsinoo cy/A is constant. 

The most ratioiml method of roprca<miiii|jf 
graphically tho oxpttrimental resultrt roforj-otl 
to above would 1)0 by plotting tho 11011- 
dhnonsiounl term It/lkt) im thu non-diii)eimii>invl 
l)aso \/{Vuji>) or \t(aVv/k), from whiitb, if t-lits 
above law is exact, a straight lino would !x* 
obtained oliaraoteriulie of that parUoulnr 
of wire. 

(32) DYNAMICAL RIMILAWITV. 11 
bo remarked that if V//c and OcfpV* urc* 
mamtttiiierl constant from problem to pralili'sjii 
tho system of strcn.ni lines and stain of f ; l>^v 
generally will remain goomotritially Himilfii-., 
for the velocity v at any point gomn o trivial I ;y 
fixed with respect to Uio body will bo of fcli"c 



form 



V 






and tho argument follows olosoly that ad<(pl.n| i 
in tho oaso of tho motion of viscous /hiifiw, \ 
alromly oiitlincd. ^ 

More recent investigations of tho rato rf I 
cooling- of wires in a. ourrent of air, ly TJ. V. \ 

.soil, Pfiil. Mag., 1010, xx. fi!)l. *- 



DYNAMICAL RTltrLARF 



ho-vo n]u)\vn lhi> present of another 
)<>Hi<li'.H tlmt involving V ! , vtn. a toi'in 
Lidiinl to I,|KI .Hipmre i>f Uin linear tlimen- 
>f Mm lint body. King in fact found 

HOMO nppmxLintilion to the results ho 
id for llio rato of boat transmission was 
ly 1.1 K! nmpirioal formula 



A, 
dni" 



H, tmd arc conslanifi for the 
#in utitl shapo rif wire e-ircnlar in 
m J... !''. UiolmrdHon a has miggraled 
ho proanneo of the torrn r.(0'~ O a )lrt 
I'.H tlmt Mio volomty noar llio lint body 
]y iirmliKH'd by tho rising of iltiicl duo 
nut, I oxjmnsioii. It, follows, fhorofuro, 
m niMiiul, tliat f.lio ntkUtiinKil l^nti 
to Im nxjmwHiblo in tonna 'of the 
riiifcci Hi-mip alrauly rofern-d to. vi/.. 
/fW. 

) JMnHK AciciuiATi.; DKTKKMINATION OF 
M. \Vrithig 



' "c, ' dii, 

I (Jii rliiii(>imioiiiil niiinoiiinj,', nml 
thin to U! onipintiitl foniiula fuiiiH] 



, .. 

h ' c, da 

Iksivtal tUat tlio form u[ thci fumtium / 



I 1 , <,*, iiiul It aro now mwo 

inncl Hciloly hy UmfjjcomotmiiLl 
.ivorwully a|ij)li(iiililo for any gun oiuso 
IICH of tliiiHt) (Juno iiuniljui'D huvo Ix-on 
f n mi King'H 
formula in 



rtilutiou Imtwomi tho nito of lioafc 
tin! uuiiainiii^ quiinl.itic'.i /, oto., 
'O not pi'Miimod vat'ial>lo in tlio 



I N<)W-l)lMUNSIONAIi C.KOUl'M AUK TUB 

'AiiTAW.KH.Tlio roiil variables in fact 
problem nro tlio (lojiondoiit 11011- 
inu*,l quantity h /!!:{ I) -fl ) and tho in- 
Nib iitm-tlinHinnioiml groups Vc//r imd 
vJiil tliu niosb rational gruphical 
of tlio cxporiiniintal remitls 
lio tiliLjiinod by uliowinp: tlio law con- 
tTio variation of this dopimdwib 
i ivilli imuli f thcHo iinlopcudent 
!.H, Lho Hyatoin of onrveH obtnimid 1 icing 
iiiriKsfau'LHMu of thin tiliias of probloni, 

. Trfinfi. \, HH'l. nixlv. :17:!-IH2. 

- l*ftf/X. Nl)f.. XSNll. I't. V. -KHl. A lllrtl'llHHlllll 

K]ii'r1ii!iilal ri'HiiHs nf inniiiirdim wfii-lH-vs In 
mi (-ho Hlntiilpnlnl. of Ilic pn-flcnt nfllnlc by 
ivlrt, I'Jiil. Matt., I'm:, 1020, xl. 



Y, THE PRracrPM'IH OK !H 

and ilopomlenb only on (,ho gconict-rtaal con- 
ditions. 

II, DIMENSIONS OK El.TlCTHK! AMI) M A(l NT/l'IC 
QUANTI'I'IKS 

(JIB) Ki.Kin'HnRTATirjs.Tlio troalnu'iifc of 
elefslrioal and magnolic. phenomena from flio 
Htaiiil])(,in(, of tho prcHent artinlo pix-nenls HHIUO 
points of inloroHt. (.'onHidiiring in tho Hirst 
jilauo i^li-iitroHlatii! fpimititioH, wo possr-ss nl 
pnwont no means of impressing elc.olrie or 
niagnisl.ii! eharffi> dircully in ternm of any of 
tlio fimdami'iil.id units already introdiii'cd. 
Aooiu'dingly a eoiiHidoration of rldntroslntin 
fjiiantitioH must introdwio a m-.\\ r nnif, direolJy 
related to tho ohnrge. Tbo simpliwt iiietlinil 
of roproHoiitation is tbrongli tlic i|iianti(y K, tlio 
speeilK! EndiHitivo eapricity, and tho' e-xjieri- 
niontally known law of form between charged 
boilias. Aecrdintf|y wo wrivo 

1 t-f-'^f 

K r* "" ' 



At, oiiisii, from fho dolimlinn of tin; qnnntilms 
(idtKKsriusd.it iHpuHHililolo dm.\v \\\> the follnwinu 


(Jinuitlt.y. 


Sj'inhul, 


Dliui'iisldti, 


(Jlutr^n .... 


i: 


KUiM'r 1 


Kli'olrio itilciiiiity 


I' 1 


K' ^i\i^i,"^'r"' 


I'liloatiiddiircrcn^it . 


V 


K-iAirJ-r l 


('niTctit .... 


i 


Kimij^r 3 


IfctHiHlniim . . . 


.H 


K.- l ir l T 


('aj)aoity .... 


(i 


KL 


S]trailiaiiln])p]nli;ii|, ) 
iMpiidily / 


K 


K 



In tlu) Htiinn innnnw, (iinnnuiiuting with tho 
doflnitlon E nmjrnoliu ]iormoaljilil.y ft, OH 

1 nun' . 

-for, 

H r* 

m niul m' being Ibn Htn^i^tb of twd 
magnolia poles, wo can draw ii]i u jiitralldl 
list of quantities) involved in nni^ncitid 
plionoinoiia, c.f/. HtronijUi of niajjimtii) pulu linn 
diinunsioiia /^iM^Li'l'" 1 . It, would nppNir itt 
first nielli an if tbmo twci Ymitt M-oro <|iiito 
in (loiiom lout and that two Bopaiulo iinUn, 
K and /t, for Lho ilisoiiHainn of (doc.l.rio anil 
inagiiolio phoiuniioiuv would rcrpiiro to lio 
intrmliHsutl, Imt it is known thai, inn^n^lii! 
and uhiotric iilioiiinnona arc uloHoly iiitonv<ivoii, 
that einrmnlH flnwing tiirough wires wifiinnla 
nuignotio CuMa in tb(tir iKM^hbinirliood. 

g (Ufl) KliLATfOK IIUTWJ'IMN KLKCTII KUI.. AH11 

MAONKTIH UNITH.-.-WO bavo in fad, thin 11011- 
otin^ link, l-hat if a niHgmtl.io polo nf HtmiifjLb 
in made to (hro!i:l a oironit oime, in wbiub IH 



DYNAMICAL SIMILARITY, THK PBlNOrPLES Off 



(lowing a current of -strength i, tlio total work 
done is measured by 

work dnno=<t)nfti'. 

Itorico tlio dimension of tho product of mag- 
netie, 
of work. 



, of rCTlatnncc II anil imluola.ice [ imlu* 



a inaxiiuiiiii cunx-nt givon 



KM.F. gimi l.y 



]'t. it iS 
a "|~ l 





Tho moat natural Htnndurd volooity to adopt 
in such oil-mimfltanuca would bo tlio velocity 
if uhwtro magnet ie waves in tlio particular 
medium, and autM.rdingly wo hnvo tho relation 

/ilt-A/V*. 

whore A ia some con.Htimt which accurate 
exitRrimcntal investigations have, in fimfc, 
Rhown to bo oriiml l<> 'ty. TI H flll "l" 
yot fundamental rolntimi between /<. and K 
enables IIH at oneo to redue.e tho two systems 
of unite to ono, either by expressing all tho 




The lot ill energy of n clinrgo e. of dimension il moving 
with volocity in a mwliiim of coimlanlM 



und fc 



nr units iii (iiii-'i i:ii''' >v "-i - , , i i i 

ILlric.nl quantities in terms of nmgnetie Tho radiation It from W i acculnratod elu.tum w 



units or vice versa. Wo express them hero in 
terms of electromagnetic unitH an follows : 



Quantity. 


Symbol. 


Dimension. 


Clmrgo . . 


c 


AuM ^ 


]3lentrici intwmity . 


If 


nhi*d"K~* 


Pottmlinl differenoo . 


V 


/^iJ-r 8 


GiirriHit . . . 


i 


,,;hih^- 1 


Ui'sislftiiBc . . 


It 


,,uir l 


Cfijmoity 





A -'f/V 


^iiy'" 1 ' ' 111 "" 1 ) 


K 


/r'r/V 


Siriingllnjf ii]|ignulio\ 
polo ( 


m 


^Mh>r-' ^ 


IFngmslJo fiiren . . 


]I 


^rhi'r.-'ir 1 


Miignotio inihi<!lii)ii . 


1) 


^iiii/ir 1 


Mn(jiiotio pcnni'a.bility 


H 


^ 


CoDflioiont of induct- 1 
anco J 


I. 


,uL 


Jiy meanfi of these dimensional relations it is 
possible oneo more to group together whole 

i f . .__..j.! jl.-*..'. rtf i}m mtwlnnf tin I'.llfl 



variation of certain non-dimensional 



whom <i=accclcration, and tho radiation ia imsumcd 
indopuiidont of the diivmolur of tho eleotron. 

III. TlIK Al'I'I.KJATJON Olf TUB I'UlNUU'l.lW OF 
SlMlLlTUDll TO JIOIIEI.S 

(38) MODEL EXIMSHIMMN'IS ANI> TUMI it 
FULL-SCALE EQUIVALENTS. Tlio 
dovolopotl in tho foregoing 
Horving na they do to group logothor |inieHfHsa 
ocourring in gconiotriually mniilar HyHttsniH, 
provide tho most natural method of appi-mush 
to tho problem of tho rolutions of niodclH t(> 
thoir fnll-soalo countcrpartH. Tho linen of 
dovolopmont in the cnse of tho UHO of models 
for tho determination of tho wind foreen on 
aircraft have already been dmoiiHHod. Two 
further aspects of tho general qmitition will 
ho hero treated. What, in the first pliioo, Jiumt 
a model fulfil as regards working condition;! 
in order that its motions and working may lio 
directly comparable with thoso of tho fnll- 
aiKod maohino 1 That in to way, what iiro tho 
rolations between weights, oxtornal fortniH, 
speeds, ote., that two systmns initiaUy 
geometrically simitni' may continue during 
thoir motion to remain goomotritially Himilar, 
that tho relative jxiHltious of the parlH of ono 
system after a time I may ahvayn be similarly 



r!;;;^r,='= 



tho roaitlta uhtainod. 

(,'17) Ai'iT-K!ATioN9.""Tho following sefoo- 
tio'n of Bimpln niHiiUs can he dmlvod directly 
liy (.ho melliod of thd [wcHcnt nrtiislo. 

^[.'iiiid takftii fr a mmrnl. in a oirenit of ruBistiiiuso 
11 and iiidiiiitniKro L to fall to n given frimlinii of HH 
iuUnmily wlicn Hwilnhcd off w |iniii(irliciiii] to T,/It. 

A ]](ivi(nlio KM.R of any form vvh<m ainiilitudd 
is iipiioifk'tl hy K and period Zwlp noting on imy 



sponding jmrts at timo //, where ( aiul (' hoar 
a coiiHtant ratio to ouch other. It is dear 
that if theso conditions eau bo dolerniined 
and a model produced to operate salisfiiulorily 
while working umlor them, then tho full- 
Boalo maehine will al.so opcmffl HiitlsfiUitoi'lly. 
Tlus aeconcl aspect, dealing with the wtrongth 
of eoiistrnotion of tho moilol and ot tho fiill- 
, will ho treated shortly. 



DYNAMICAL SIMILARITY, THti PlllNOrPIVKS OK 



S (ill)) CONDITION FOR (JON'L'INHKI) KlMTI.AH' 
1TV IN WOKKIMO Oh' iUlimJIi AND I'\TI,I,..SCA].I-;. 
-(,'or respond ing to each part of tho Hy.tUjin 
thero will IIP a scheme (if equations between 
the moving forces and decoloration produced, 
of the form i((l s .K/dt*) X for the model, and 
fur the fiill-siKdd nianhino H>.'(<?V/(/J' :ii )-X', 
whoro m anil m' aro tho musses of correspond- 
ing parts, ocou] jying corresponding positions x 
mid a;' at corresponding times I and ('. X 
and X' art! tlio corresponding moving forces. 
l<'or oonl.inucd geometrical similitude at time 
j and (' connected by (~TC, where 'I' is some 
constant, there must ho x-~lx', nt~~Mi', and 
X 'KX' whore i, M, and ir aro constants 
determining tlio scale of the ono with reference 
to tho other. 'll'onec, inserting these in tlio 
first equation, 

Mm'/ fV -, 



ami tlio motions will therefore remain' identical 
if j1/7/'l.' a F--l, tho same e() nation then apply- 
ing both to model and futUaeale. "llonoo (ho 
moving forces of model and full-scale intml- he 
in tho ratio I' 1 , where 



In (hoHnmo way, had tho corruapouding timou 
l)oen ellrninuted by ooinpui'ing tho systems al 
c,oi'i't)H]ionding H|icedn wo would havo found 
that for similarity tho moving forces must ho 
proportional to i\IV a //. 

Tho following coimlnsitmn mny ncnordingly 
bo drawn for a comparison of tlio working 
of a model with that, of the fnll-m/,ed nmdnno : 
Hint'O tho weigh tN of tho parlvs, regarded an 
external forcoH.aro projiortionnl to their maHsost, 
V a '---=/, and tlio volooity of working nuiat ho 
proportional to tlio Hijiiavo root of tho linear 
dimensions j external moving forocn miint 
lioar a oonHfcaiit ratio to the weight and must 
therefore inercaso as tho onlio of the linour 
dimoiiHioiiH, if model and miiohino ai'o made 
of tho same material. 



IV. Sistu.iTUni! OF 

ij (40) K'rittJOi'iniAi. STIIKNOTH. Turning to 
this question of tho relation between tho 
Htniotnral strengths of models ami fnll-soalo 
eons true lions, it is proposed to show that tho 
theoretical basis of model strength teats on 
Btructnros may bo developed in a rigorous 
yofc simple form by an application of tho 
method of Dimensions. 

When a homogeneous prismatio strut of 
length I and floxnral rigidity KI, simply 
supported at the ends, in subjected to axial 
ond thrust F up to a load given by 



t!io iindelloctud positinn in one nf 
i|iiilibrium ]U'ovideil 11m nltimtdo jitrcwn is 
nit cxcsecded. Jteyond thin so--alltjil KuLnA 
Orilieal Loud, the 'straight pnsition in ono of 
utihtfthlo cqailihriuin. If tliu sf-rat ho<lclLe(.!ti'(3, 
us long as the loail is iniiinlaincd tho IIXLH 
will ooniimially undergo ohdiigo in f)hn[i(i 
until it ultimalely taken it]) a form of 
clnstica. During iliis jinninm i\w yichl ]iointi 
>f tho malei'iid may ho exceeded and tlio 
maleiiid may rupture. Tlio tral may tlniH 
bo mippoai'd'to fail for two }mHmlh) rei>Honn, 
.n tho ono liaml hceuuHii ils shnp bus bci'ii 
]ieniidnently changed from tho slTuight 
lormal jmHition owing to tlio insluhility of 
that piwition, and on Urn other hand ImrmiMO 
tho actual material has failed to withutmiil tlio 
sti-caseo (uiginated. Thin tMincis]itiim in "E 
course not limited to mmh u Hirnpli! tnicitui'o 
as a Htrnt, for it may ho scon tliat in gi'iusnil 
a framowork of any kind nmy fail fur oithor 
of these two reiifsims. It is proiiiised to 
investigate what information may ho funuln;(l 
regard ing tlicse two typi-9 of fitilnro, i'ii])tnr 
and inalaliility, for a atrHeture in f^i'iitsnil, by 
an a|)]>lieiition of tho diniDiiHioanl tln-nry. 

f'onHider the cs of a Hli'iiciure of tin) iy|m 
of an iieropluue framework for di-liniicHci'n, 
although the argument in rpiile gotii i rnl f \vlirrn 
it is supposed that tlie (iHHiini])1ion(i niiulo in 
tho ordinary hoiun theory upply In evri-y |mrt. 
Lot tho length of ono pail, miy a lisi.y, l- given 
by /, the area of a pnrl.Hiulur Mention hy A, 
iiloiiiont of inertia 1, and Iho elfiHlifity tuuj 
doimity of tlio material of winch it. in tfinnpomsd 
'K and' p rospoi'.tivcly. (iivi-n thcao (|iianlilirn 
for this ono jioiiion, it will ho awuniU'd iliui 
tho Hhapo and /oinneti'y '>f Ilio ntnirtiird 
involve an oxant (modification of hn\v tn dorivo 
the corresponding (niantitii'ii (or tint roriiaiuhiH 
portions. Lot the oxtenuil load 1m I 1 ', applied 
in soino given maiinor sjicciiUsd g<;inii(if.rii.tii]]y, 
and suppose this is suflioinnt to ]>rii(li[ce a 
filroaa just greater than tfm yitild Htrcwii / 
in tho material of tho weakest member. \? 
can only do]icnd njiart from tho ^ciiiimlry 
and mannor of application ti[)nn thti qinuititifji 
onunioratod above, defining tlio pro|n'j'tirn 
of tho material, These uro an fullnWM : 



Quantity, 


Kyinhitl. 


i\l/LT a 
I.- 1 
L l 

fti/i/ 1 


Young's modulus . 


A 
t 

I 
i> 
f 
If 


Moment of incrllii . 
Length .... 

Yielding ntvPHH . , 
firiivlty . . . 
Loud . . 


Since V, tho load which will OIIIIHO eolljijim 
by rupture of tho material, iniiHt itivulvi 
these quantities groii]ieil tngethor in midi t 



DYNAMIOAI, SUHLAKITY, THE I'lUNCCPLlSS OK 



nin nticr i\n to timko tlii) dimensions of tho pro. 
ditct iibiutiiijil with MUIHD of V, wit ina-y write 

I'^V-tU. A, r, /, f, f, </). 

Ap|lyiNjjf tho method already used frequently 
in MUM (JiHiiiisrtion, we easily find 

,, I'll 



I'll) 



win 1 1 'ii i/' fur tlu> inomont in an arbitrary 
fiiiKtliiui. Writin 



HO Mini, Hi in rptantity may lie considered as a 
n<iii'ilitiit,tuiitnittl iTilhsiil loading coufficiont, it 
foUowH linally that 

F' /A' ?' 

IliM KXHJONAI, < !uri'll,'Al, 

It in rlnnr from tho definition 
of if, Mint fnrjt (^ivoti Htrue-tiiro wbore /, I'l, and 
I nrti known r/i in uniipit'ly determined whoit I 1 ', 
(fm Im-altiiiK loud, iti found, HO that tbo clifi- 
iniHHiiin <if unlliipHo hy ]'ii|)(iiiL' nmy wiiinlly 
well ho nitni.nitl niinid (ji. Lob it be oloarly 
lunUnvtood thai tlio oxiust form of tbo function 
i/' uhoyn di5]HHnlH only on Iho j'Ciriinoti'y of tho 
Htruotiiro, iiH-lnditi^ ttio mtinnor of loading 
mid tlio liiw of ditttributiim of matnrial. 

l)t of tlio j^morul C,|HHH of framework 
embraeiid iu thin (liaisuHHion HO far, lot thero 
lin i!i'l<!<'fed_ a HorinH of which nil nieiulioi's 
HIM idtmticiil witli rospeot ti> nxtei'iml Hhnpe, 
dilTorin^ only in msalt;. 'I'biH ini]ilie!i that A, 
tho mm of M'oHrt-HCuition of iiny soleeted pnrt, is 
jH'oiiorlional to !-'*, mid I to f 1 . Mir thin series, 
thnrcfui'ti, A// a and l/f 1 aro otuislnnls depending 
only on Uio ^romolry, find fieuwdingly tho ox- 
[irtiHHion for i/i now inked tho nimpliliod form 



II is uol> dillioult tn tfivo n i n tor p rotation to 
Mid U'o non-diiimiiHioniil fiiKHLUtidH //.!'! and 
U'/jfA, Tlio fnnniti 1 , Imiiif; tlio mini of Uio 
yielding HtroHH |.o Yiuin^'s niiKluliiH, nmy lui 
Lillian IIH Ihw utiuiii ul tho yiiild jmint, on Uic 
HHUH motion that Jliiokii'n Law ii|i|>lic!H rignr- 
onuly nvov Uio wlmln mnj?(i. In tlm HIIIUO wny 
W//A in tlin rnlio of tho weight uf a iiartioular 
nnmihw, niiy Iho wcultoitt, to tlio muximuin 
tciiHili) (HMsiiiniircsajiivoforoOj (is Iho enso may bu, 
wliitth Mint nuniiliut 1 IH uiijml>] of witlmtimding 
wiUmiil. yielding, nHrtiiininfj; tliat tho sootion A 
lit l.iilu'ii jil Hi (i {utmtiim <f oolln|)sc. 

jf (<\'Jl) .NOtf-IHMJ'INHniNAT, VAKIAHIiMS. Aft 

far JIM 11. (IJNminmim of tho bronkiiig load 
iioolli('iciil< i/t'- 1 in (!()jinonic!(l, il in ovidwit Miafc if 
it Hcrii-n nf guimititrHiiiIly fiitnilfir fltnioturcs bo 
jii-lcufi'il, I.IVD disl-inril mut-diinoiiwiiinat vnri- 
ulilcH, find l\f<> tnily, fiiiKdioriH of Uio nmtorinl, 
allVnt l.liiKjiictilioM. 'I'hifHKinxi Mm Htrain o.fc llu; 
yinid jjolut fur tlio Wfijikosfc inomlim-, Jim! tins 
ratio of Uio woijfht (if Utftt inoinbor l<> tlio 



inaxiinuni tcuHi] oi' coinpiTSPivo foi-c-i* *''' 
win witlistiuiil t tlic point of yield. .]), it* 
i!([indly clear, lioM'dvor, tliat tiio Hi>-oull'**^ 
goonn;ti'i<;al restrictions determining tho dis-!- 
Irilintion of tlio eoiiHtanlsi of tlio mnfciJn '*"* 
in a composite ati-uctiirc are not (ibaolntcl.V 
vital to tho nbovo disouMsion, BO that violnl.ii>' 1 *'* 
of fclio laws ckilotniiiiing tlio selection of tJi<* 
matoriiil from iiumilmr to imsmhcr would n^>* i 
]K)(!(!3Siirily vitiati: tlie coiioliiHions arrived i"-*-' 
bore, ll'in' (ixanijile, nno would nut IKS ri^ni'- 
oiiHly ontitk'd to vary I, A, and K in 
moinboi's, Hinne ftiusli a cbaiiyo would 
upaot tlio yeomotrical Kiniihirity (if Ktia 
the (liotriliiition of force, with tbo 
mmilt tbnt tbo proviminly weakest 
might now not remain suoh. No Hiidi tnmbl s * 
bowdvor, could di'iso if tho Holec.tirm (if t-lit* 
nnilcrials wan iiuido without ohanging tl' M ** 
fiui tors, but allowing fi variation in/, thti yioltl- 
Jny sfcrcsfi, no Ions; 11H ^ n " ]>rvirniKly woalui-nL. 
nioinbi.!!' alwnyn roiuniiiB HO in llm HOHUH. Tl i i ^ 
JH equivalent to an increased latitude in fins 
e(j()[io of Belcotion of nmtci'iiil, 

(ionorally in oxporimonting with a moil* si 
i)C tins nntui'0 it in convenient, oE ^OWI-HO, !** 
liavo corrcapmuling parUi in tho inodol tui<l 
tho full-Male nti'iictui'0 eonniciscd of idontii^i-1 
matorinla. If, for example, tbo framo of nil 
aoroplaiio was utuloi 1 discussion, wires in 
model would bo composed of tlio sixmo in 
iif) llioflo in Ike original ; corrcsiionding 
spars, ribs, etc., of the sumo wood. 

Since tlio quantities /, 15, I, p, olc., in 
oxnruHslons for </i a all refer ultimately tn 
Baino part of the nioilol v lo tsnsuro gconidiri^iii 
Hiniilai'ityiu tbo widest sense itfullmvs that Ui* 
assuin]Jticiii that//K is a cuutitant in ono -\vliinli 
is obvious oxporim en tally, Under thcao csir- 
ounistancra also W//A, as enn easily bo voriliin I, 
lnieiiniCH j)ropoi'tional to the; linear diim>nnimi /. 
Tho liroiikmg load cocflieiout </' 2 . thoivdn 1 **, 
\i-bon the woigbt of tbo striioturo tsoiitribntoH. 
tnwards ni|itnre, ia purely n function of /, 

.-. v- a -^i<o. 

and tho form of tho function is detenu inotl 
only by tho shapo of tho various partis Mio 
geometry of the loading nnd tbo Ho-imlNic I 
gcoinotry of tho material 

{'!!}) ihlMITINl! iSlKK 01-" A ITKAVV S'l'lilro- 

TUBE. This expression for tfi* may likovvlsn > n > 
Wpnosecl solved for I in terms of r/ ( a . .ll'iir vvttry 
external load coefficient this equation them 
dotorminoB tbo siao of t!ic elructuro corresjinml - 
ing to failure. Wbon there is no oxtertuil Nm-cl 
and failure IH duo to weight alone, j/j,(/} ; -. <), 
an eqimlion determining tho Hinalle.it tiixti *f 
a structiii'o that will collap.so under its (iwri 
weight. 

When tbo material ia not RiifTieiently boav_y 
to involve tlio weight of tho structure Eipprnrti- 
ably na a factor in causing collapse, the torju 



DYNAMICAL S1MILAUITV, TKU PRINCIPLES OF 



Ofi 



W/fA may lie omitted in tlm general equation 
mid Uiii expression for i/> 2 takes tho relatively 
simple form 



('14) NON - mMHNSIOKAL BASES, AND 

" (.'HAU.UJTEIUSTIU CIJUVK," Lot iiH imagine 
tliut Iho weakest member in replaced by 
another nf tho Hiimo gcomotrreiil aliapo mid 
KJ/O luil with a different viilno of f/K, though 
not HO dilTorent an to prevent ita remaining tiio 
weakest member ; then u test on each one of 
these models will give a particular viilno of s , 
breaking loud onofliiiioiit, and these when 
plotted against f/K will give a " elmraeter- 
istij eurvo" foi 1 tho structuro of tho given 
geometry. For geometrically similar struts- 
tim's of whiu-h Iho corresponding parts are 
made of tho snino material, so that //E is 
constant, tho broaldng load coefficient becomes 
an absolute constant for tho scries depending 
for its valuo purely on the shape. /( follows 
t/int a simple test In destruction on it mottel will 
suffice 'under Ikexc amditions In determine, the 
lire.nk.iiKj hind f.w,ffn;\e,nl </>-, and therefore tho 
breaking load F for any other member of tho 
series of geometrically similar struetoiros. 
{'(il) Kuuiiii'! niiMTi) .IN.STAKII.ITV. -It SH 
in thin Hectioii Mint the failure is not 
rilj' neisonipaniod liy eolla|).ii) or vuptnro 
in tho iniitL'viid, hut iH duo merely to iwrmn- 
nent (information of tho donfiffiiratioii of tho 
HlriHsture. It follows Unit, in tho ex]m:Hrtiu]i 
for tlin m-itioal load, t!io yield sfcross (Lous not 
iMilor nltlioiijrh all the othor toi'ins A, I, 1C, I, 
/i, t! "iiiy do H, Using <^ a us a critical load 
ooollidiont dolined by W/KI 0V then 
A W I 



oblaineii by tho nnmo motliod as in tho previous 
Hontion. 

On tho undomtaiiding that tho struct nres 
in tho Hories aro all ^eoniotrically similar as 
I'ogards external Hha]jo without reference to 
niatorial ooniposiiif; tltem, then A/^ a and J/i 1 
aro (ioiiHtiiuts for the seri, and 



wlioro W/KA is tho ratio of tho weight of a 
inornbor to the lonsilo or (jomprcssivo forco 
rei[iiii'eil to ]in)dnee unit strain at Homo par- 
tieular flection of that member. 

If corresponding members of tlio series aro 
made of tho sixmo material, then W/KA ia 
easily HCOU tn ,bo proportional to I, from 
struetiii'o to structure, and aa hofnro tho 
oritioal loading onnftloicnt 

0" = ^W 

depends on tho sine only. 
{![>) CKTTIOAT, LOADINU OOKI-TKIIKNT A 
T nni Cou-Ai'SB wuu T IN 



\Vlic]i the wc.'ight of tlio atructiiro JH m-gli- 
giF>lo as far as its cifl'eet in cunti-ilmtiiifr lu 
failure is concerned, tlio whole instahility 
luising fi'fiui tlio csxlei'iinl loading, iben <ji* 
is a couiitimt for a KDI'JCS of Hti'iictni'ra nf 
identical form irreHjiootive of the aimlciriiil 
of which it ifi composed, find tent to ilcsh'nf,- 
lion on one intxlp.f. suffice. 1 ! far tfte series, 

It lias iioon found that the eriticid loading 
for a uniform prismatic, strut of 
weight under (sml th rusts iimL siiajily 
at tho ends is given by 



ao that t/i for tbis structure is ?r. l-'i>r u Html, 
under tlie same eondilioiiH, but with t'laiujii-d 
ends, $=.Zir, 

Tn certain cases of shnjifo shaped nf 
structures, it i.s obvious that tlus function ,(> 
may be derived by cnleiilation, us for oauiiplo 
in tho above two fuses, but for imiro cornpli- 
cated problems whei-o tho calculation in tun 
abstruse a number of points en tho chtiriusd-r- 
istic ourvc may bo derived by n snrion of 
touts to destruction on models. 

In the a[ie(siiil <-!iK(;a whims if> is a coiwtant fur 
tho soi'itsM 11 Hinglc, ti'.st on one modd is clt'iirly 
sudieient. Thin, as has boon shown, nppHi-M 
with equal fonso where tlmisallnpimia due cilln'r 
to instability or to hiiluro if Iho material. 

Tho basis of the experimental intitbnd Mum 
having been inadn seouro, no Hcahi dUr<i|. 
diHiuulty of Lbo typo normally ai'tsing in, nuy, 
aorodynamia ivorl; licinji? jiresonl, it filinnlil 
now bo possibles to ]nceed le n direct aetiiintln 
tost of failure anil ils causes wmtor vurjimii 
ciroiimstunci'H. 

(i7) WiiniT.iKOOFSirAras. Wliiie the- fine- 
going anatyais applies to sli-uoturcs inidrr 
forces of tho statie typo, IL parallel 
can bo applied where lUioiiuiting 
introduced, or whore parts of the 
aro in motion. In illustration consider the 
problem of whirling of a rotating abaft of 
given outline and section, As before, Hiippo:;n 
Iho geometrical slmpo longitudinally ami woid. 
scctioiially to bo given, length I, mass |ii>r unil 
length in, and floxuvnl rigidity of a partiniilur 
scotion EI D ; tben if q lie the Hjieod of roluCion, 
tho deflection d at the (sonbru, say, will fju a 
function of I, m, E, I , and q, i.e. 



TT 

Honco 



on equating tho dimensions of Iho lyplcul 
groii}). .For n, shaft of given guoiuotrliml 
onllino ]/(' in n constant; <Ippentk!]it on tlm 
geometry, hetieo in varying tho si'/o of \y\\i- 
motrienlly Himilnr aliafls tlio raiia of tlm 
dofloction at the centre to the- total length will 
depend only on the quantity )qH- l jV J \ ll . 



DYNAMICAL SIMILARITY DYNAMOMETERS 



VARIAHU-I. If 
whirling speed exists, then, for sonio value of 
q, tho ratio djl will tlieorotiwdly become 
infinite, or at least indeterminate, and this 
can only occur for some value of tlio variable 
wig 2 / 1 '/ HI,,, say a. Hence we find that tho 
real variable in whirling shaft problems as 
the size and material of the shaft are varied, 
but maintaining the geometrical tthapo con- 
stant, is jwf-C/KIo. In actual fact tho whirling 
npeod of a straight shaft jg known to bo 

/J5I 



_7r a /J 
-' 



and for a homogeneous eirmdar stepped shaft 
mado 11 j) of threo portions, the two end 
pieces of kmth //I and diameter rf/4, mul tho 
central portion of length ?/2 and diameter <J, 

)?'' o 
'j.ii '*> 

J'llfl 

I being taken Mr the ccntml portion. 1 

from tho foregoing analysis, more-over, it is 
apparent that shafts of identical geometry 
but differing in si/.o and matorial will maintain 
their identity in geometry under rotation 
provided they bo compared at corresponding 
speeds ft and q a given by 



a / m \ _, 

V Eji'r 



v 



(49) KxPANsifiM IK TKHMS ov r nrn CLASS 
YAUTAMLES. It Jias boon mo apjmrout in the 
application of thn method of tho present article 
to various bivwiohos of jdiyjics ami onginoor- 
ing that in all onana tho investigation has 
centred iteolf muntl tlto bodiivtour of soino 
ox[iro.ssi(m represented an ti funetion of a 
ourtaht iioii-diintuisioiial group of twins. Tliis 
fjiiantity, ooiinooting tngothor 3 it were ft 
wfiole class of prohtoms possoaaing certain 
geometrical and dyimmioal Htmilnritics, may 
bo termed tho dans variable. Many problems 
in malhomatioal phyaics oxproasiblo in tonna 
ot d'ifiorontial equations would appear then 
to demand a solution as a function, of tho 
class vaviahlo, and nconvdingly an expansion 
of tho solution of tho differential equation is 
sought fur ns a power nodes in tho class vavi- 
ahlo. This method has boon Applied with 
(ioiiairtorablo Buenoss to tho problem oE tho 
crippling of struts, tho whirling of shafts of 
variable flcxunil rigidity, and to the motion 
of a vfsooiw fluid. 3 In o/focfc tliis is simply 
un analytical method of roprosonting tho 
" nhnrnotoriHtia curves" on non-cHincnsioiml 
bafius ohtainorl BO frequently in the fore- 
going disoirssion. ity. r,, 

1 Coivlny ami Levy, 1'kit. Miff., !!)2I, sit, fiOH. 



Experimental vorilieation of Haylcigh'H c:on- 
diiiiMis foi 1 the nwt'ion of i]ii)iln in mmlnuk 
with solid bonndai'iea. Rue ".l ( 'riction," 

(10). 
Rayleiyh's method of determining the 

essential conditions which must l>o ful- 

filled. Seo ibid. (15). 

PYNAMHJ.S, I'AirnorjH, ATI'LICATIOK OP DYNA- 
MICAL SIMILARITY TO. See " Dynamical 
Similarity, Tins Principles of," (7). 

DYNAMOMETERS 

S (!) FITNUAMUNTAT, PmNiJii'Lilfi. Tho work 
dono by a pi'imo mover or other ugwit when 
transmitted by a I'otating Hhaft may bo ox- 
prrased by 1'Hi/j, and when by n mtivijig 
chain, rope, or mtmhir ngent, by 'J.V/, whoro 

V is tllG furf.'(5 ai)ti])g, 11 tJlfi tOHJllO Jll'JJJ, ij> 

tho angular displueeinctit, and tl the linear 



A dynnmomotcr ia an instniment which is 
iiflecl f<ir tho inenfitii-eiHcnt of tho foreci J', or 
the toi-qno Pll j tho values of tho (piantitics 
tfmniltl are nsmilly detci'tninoiJ imJopiaidimlly. 

Tho work done by the ]H'imo inovnr may 
oitlior be absorbed by tho dynamometer or 
transmitted to a machine in which it it! em- 
ployed usefully after having been measured. 

It is necessary that the instrument adopted 
should perform its funetion with aeeuracy, 
Tho whole of Uio energy developed by tho 
])i'imo mover Hhould ho included in tho measure- 
ment mado without ne^letiting that absorbetl 
by shaft beai'injffl in the dynamometer itself or 
by gearing or bearings ivhiiih mny bo inter- 
posed between tho prime mover and tho 
dynamnmciei: 

Tho load should bo capable of I'mo ad- 
justment tififler rdniitnp; coiiclitioim, find 
this ailjiislmont should prctei-ably be over 
u considerable range of power in order 
that tho prime mover may be tested from 
its minimum to its maximum power capacity 
without the necessity for frequently stopping 
down. 

Tho coiiRfcrnotion of a dynamometer should 
bo mioh that it imposes no force on the prime 
mover other than that for which it was 
designed. For example, a dynamometer 
suitable for testing a petrol motor should 
exert a pure torque, otherwise tho motor 
bearings ivij] lie pulled upon to Inlto loaf Is, 
and tho shaft to resist bending and shear 
stresses, additional to (Jioso for which they 
woro intended. 

It is desirable, in tho typo of dynamometer 
in which tho power ia absorbed, that tho 
inertia of the rotating purls (mould ho small 
in order that a stoppage may readily bo 
effected if failure of tho prime mover should 
occur, as the energy stored in a heavy rotor 



DYNAMCHEETKRS 



revolving at a, high spend may bo sufticicnt to 
caiiKO vnry sorimis damayo. 

Tii order UuiL accurate measurements may 
lio mn.de, it in es-ioutinl that the dynamometer 
should apply the load extremely steadily, 
otherwise violent oHoillii-lioiia will lie sot up 
rendering Iho employment of heavy dash pota 
noi'esi.'wry, which IN undesirable. 

The variation of load with speed for the 
ftamo sotting of the appiirutUH should lio such 
Unit " hunting " of tlio load is eliminated, 

(i.) AbtiorpHon Dynamometers. In these 
tho onorjry generated is converted cither into 
bent by Iho intermediary of. solid or fluid 
friction, or into electrical energy l>y means of 
a Konorator, 

Tho apparatus in moat common use is the 
fluid friction brake, this being simple in 
construction, easy to regulate over a wide 
range, and oxtromoly sternly in action. 

The solid friction hrnko for largo powers 
requires considoniblo experience in manipula- 
tion in order to avoid unsteadiness duo to 
violent simtehing of tlio load. In its simplest 
form for small powers, that of tlio rape hrnko, 
it in a very cliieusnt ami aconrnto hrnko ami 
runn very steadily if proper precautions arc 
takon. 

fii.) Trnnwiftston .DifntiHiuiHctMs, for tho 
nu'iisuromont of power transmitted by n shaft, 
exist in Ihreo fairly common forms, vi'/,. : 

(1) Tomionmotni'H, in which the anghi of 
twist of a length of the shaft duo tn torm<uial 
stress is measured uithor optically or hy 
moohanicul niojuin. 

(2) Torc|iie-meU>rN, inwhiuli tho tor<|iie load 
is transmitted, by springs, or by hydmnliw 
])hnif;((r)t, tho e.xteiiHiuns of the former and 
the fluid pn-Hsmm wot up, by Urn latter being 
indicated nr recorded. 

(It) Instruments for measuring tho pmver 
tranmnitlod hy moans of a belt on the shaft 
of tho pi'inui movur. 

Tho Itisfc vary considemhly in form Imt tho 
objodt aeliieved is tho Hiuno in eueh caso, v\y., 
the mcasnromnnt of tlio difference in tension 
of tho holt on either Bide of the driven pulley. 

Another important form of tlio transmission 
dynamometer is tho traction motor for tho 
measurement of tho tractivo effort of nelf- 
propellcil vehicles. Dynamometers have boon 
designed for measuring and recording tho 
traetivo elTort of locomotives, motor cars, ami 
traction engines and the traetivo resistance of 
railway carriages), wagons, wliools, and ploughs. 

ij (2) ADSORPTION DYNAMOMKTMKS. (i.) The 
Prony Brake. Tn its original form this hrako 
consisted of two stout beams of wood damped 
upon tho ahaft or on a pnlloy fixed thereto. 
The beams wore suitably bored in order to 
grip a largo proportion of tho oiroiimferonco 
of the shaft, find tho nuts on tho clumping 
bolts served ns a menus of adjusting lha 



Motional reaiataiiuc between the ,huft ami Um 
brake. A horizontal arm, usually an extension 
of tho upper beam, supported a loud pan mi 
which the weights were hung, a line luljiiHt- 
mcnt bcm[< provided hy 11. jockey weight, tho 
position of which could be adjusted along tho 
beam. The movement of tho end of the nmi 
was confined within small limits by rigid 
stops, one above and one below ('ho arm. 
ffig. 1 shown diagram mutieully tho arrange- 
ment. 

Very liberal lubrication (if tho frietional 
surfaces was necessary to ensure smooth 
running, but at best considerable vibration of 
the) arm took place; duo to the variation in 
frietional resistance between tho brake ami 
the shaft, tho end of the arm oscillating 
violently between tho stops and rendering a 
good balance difficult to obtain. 

Tho torque T exerted by the shaft when 
tho brake is balanced is represented by Ji'K 
where P is the frietional resistance between 
the brake surfaces, and II the radius of tho 
surfaces ; it is measured by tho algebraic sum 
of tho momenta of tho loud, jockey weight, 



Stops 




and tho brake biianiH about tho centra of tlio 
shaft. 

In eiilcnliiling the horso - power developed 
thn fnotor </> in required and ia obtained by 
means of a tachometer or by revolution 
counter and stop watch. 

Tho rate fit whicli work is absorbed is 
expressed by 

2irTN 



where N in tho speed in revolutions per second, 
and T tho torque as measured hy tlio brake in 
pound .feot units. 

(ii.) JMadifuxttiann i>/ tfic Pmny limle. 
Several improvements and modifications have 
been innclo on tlio original lirako as first used by 
Proiiy. They consist chiolly in arranging lliut 
tho grip of tho brake blocks sthuH nutonialw- 
ally alter with tho value of tho coefficient of 
friction, tluis maintaining the tot^il frictifinn-l 
force and tlioroforo tho value of T more or less 
constant. 

TJio Appoltl hrako is shown in .Fig* 2 and 
ia nn example of one of many compensating 
"brakes, The woodoii bloolcs forming the bralto 
are connected together by a stcol bund pro- 
vided with a hand adjusting screw at A, tho 



DYNAMOMETERS 



(dids nf tiio stool bund ]>olni nmiii'nted lo the 
uonipmirtiiliii" I over at 11 and (! ua .shown, 
The und of tlio lovor 1) is pivoted to tho engine 
fnuiio. Tho load in supported, an shown, from 
a honk attached to MUJ ateul hand, n pointer 
hoing provided tn indiisiil-o whoii tho honk is 
lovnl wll.li llui cimtro of tho shaft. 

Tti tlio tmi'inal position tlui hook isi opposite 
l.hci jinitiloi 1 and (\w lvor 111) is vortical. 
When tlio loud in lifted, the Eovor moving about 
I) IIH eontnj roliiU^ with HID stool band and 




vii'tiiall.v irntri*iiHi!M its Ictngth, thus slackening 
tlio band and partly rolinviiifr tho loud, 

If tlio loud fulla, dun to llui (soofiicicnt of 
iKii'KiiHingi tlin ounipotisating lover 
round in Uio niniosiUt dirontion, Ugh Ions 
tlio burn!, mid thim innnmsKs I ho grii) and lifts 
MID load. 

I'll nnuiLico it in found Unit nearly H inncli 
ailjimtiiuiul nf (.ho load. JH rmjuirod an with- 
fHit tlio uoni|)finfmtinj dcvi<so, hut tlio tihiof 
iibjctiliuii to tlio bi'rtlm is Iliat wlioii n. linavy 
tnrinn) In fmiii^ numHiired tins lovou ranoia <n\ 
this fin mo with miflioiimt force to anuso tin 




(iri'oi* in tho lostdt obtained if the 
onliiiury inotliod <if onkiulation in ndontisd. 

A buttor form of uoiiipiiiiHnting brake, but 
imo porliftpn not (to well known, in that designed 
by Hlr. .Utillc mid originally used by Messrs, 
HrtiuuHiHW KJniH ami iFoiTric-s. It is shown 
dianiiniiia(.ifrjilly in !''i;/. it. 

:riii- i!ini]|*(iriiiling lovor in boro outside tho 
diHo (if (,fio linikfi ivlii'i^l, mid i.t ooiuicotcd nt 
.11 iiixl (! l,o tlid rndrt nf tho KtriLj) and tho 
loud imn in huH fnmi Iho point D. Suitablo 
f)(,opn ui'o provid^il for Uio lovor. '.Plio weight 
uf tlio Imiko luljimtiiiniit Joiul. must bis talton 



into flonHidoration in dotonnining the, lot'';) 11 *'' : 
it TiHiHt ho considered as iintinj^ at a. riK^ 1 * 11 
oqiiai to Us horizontal distanou from thn ft 1 * 1 1- 1 '* 1 
of the -shaft, and its moment must bo dcxli' 1 ''**'* 
from that of tko loin! P. 



iihn* 



'* 



Solid friction brakes may ho imod t 
Rrciircr pmvors if the wheel iw wator mi^l*"** 
Tlio nuijiii' jiortion of tlio energy \vhii' li rfl 
converted into heat in thus qnidtly din|< 1 |rf ' l " 
of, and (ino of the chief Bonreos (if lr<ni J* ( ' 
nainnly overboiiting, is then removed, Af'"" 1 ' 
a preliminary period (if running witli \viil*" 1 ' 
cooling (,ho brake blocks ansiinio n in* 11 " 11 * 
constant frietional remslnnoo, i'oii(U;i'inj, r t-li*" 1 
brnfio miKih Hteiidior to run. 

Water cu<ilin of tho whool in very nini|*'y 
ofl'ixstod by making the rim of tho brake tt'li*'"'* 
(if trough Hi-'etion, tlius enabling it lit lu^" 
wator when revolving by virtu o of 
contrifugid forces called into antion. 

supplied by a pi]m tiippiujr in|, 



trough at tlio bottom nf tlm \vli '"*'' 



loose 
Pulley 




I 



1-ln* 



I'm 




Kin. 5 



tho OIK! of tlio ]ii]io liuinH turned in tin* 
dmiution of nitaiinii. Tim miUut \n\n.f i'-t 
usually fliittoncd at tho ond whioh in diri*ol-*l 
against tho stream of water wliioli ]m MJ u vi 
round with tho wheel and out thrnnyli i Ins 
dinnhnrgc pipe. 

T-ho How is adjuatod until a riiiiHinutltlo 
etnady temperature is iittainwl, 

(iti.) Hope, Brakes. For small i>mvom I In? 
ropo bvulics introduced by tho latu I t tin\ Ki1 \- in 
and Professor James.ThoniHoii uro very mot rt^m , 
ful. Tho forinor is illustrated in ./'''(/. '1 inn I lliu 
latLor in Fig. S. 

Lord Kelvin's brake consists of u luuj* nf 
ropo wrapped round tho fly vliool of flu* printo 
mover, <mo end of tho loop sii])]>nrliii,}jf n 
weight W, tlio other being hold vorliiwlly 1 r v 
a sjjring linlanco. Worn! blocks rn Hoom^-li 
to tho ropes in order to keep thorn ])ro|)tt:rly 
spaced to jn-ovent tho ropes ,fnnn rnhljinjr 
togotlior ivhero thoy leave tho wln;(*l ( u 1 1 , 
gontially. The wood bloctka uro not iiiinil tin 
brake blocks. 



DYNAMOMETERS 



If tho wheel tui'iiH in tho direction of tlio 
arrow tho lonpio in represented by (W-ii>)K, 
where w is tho foroo indicated by the spring 
balance find .11 tho radius from tlio centre of 
th wh>I in the confro of tlio rope. 

When tlio vuliio of tho fi'ictioiml forco 
changes, the load rises or falls against tlio 
notion of the spring balance, tho brake tlnis 
adjusting itself to tho now condition. 

In lining tlio brake it is advisable to have tlio 
ropcH and wheel rim cither perfectly free from 
grease, by using now rope and cleaning tlio 
wheel rim with petrol, or else thoroughly 
greased. 

If tho lubricant is scanty or in patched tho 
weight will hunt, rising and falling regularly, 
rendering it difficult to obtain a reading of tho 
spring balance with iniy degree of accuracy. 

Tlio brake of .Fig. 5 consists 
of fast and .looso pulleys 
mounted side by side on tho 
driving shaft. It is arranged 
that a rope dipped on tho loose 
pulley hangs down over the 
fftHt pulley on one side and 
over tho pulley to which it \K 
fixed on the nUmr. 

Tho fri{!tionnl rosi.siiuico be- 
tween the fast pulley and tho 
ropo causes the IOO.HO pulley to 
rotate through a small angle in 
tho direction of rotation of the 
Hhaft, and in doing HO ii lifta 
u weight suspended by tlio rope 
hanging ovor it. At tho same 
time tho rope ovor tlio fast 
pulley, which also supports a 
weight, in, by tho rotation of 
tho looso pulley, slightly un- 
wound from the running pulley, 
thus reducing its aro of contact, 
and, therefore, its braking eA'ccb. Tlio 
sistance in thus automatically adjusted. 



the shaft at cither end but are free from it, 
and it is free- to rotate through a small angio 
in cither direction in bearings oiYoring very 
little friclioiini resistance. On both sides of 
tho brake wheel fire formed Bcmi-clliplioa] 
annular channels divided into 24 pooltots by 
narrow oblii(iK) partitions or vanes winch nru 
approximately semicircular diees inclined nt 
an angle of -to t{) tho axts. The vanes on 
one side of ibo rotor aro inclined nt right 
angles to those, on tho opposite wide, but (ire nlwi 
at 45 to the axis. The facts OH the inside of 
tke brake casing nro formed in tho same 
manner as thoso of the rotor, tho vanes being 
in tho same planes as thoso on tho adjacent 
rotor faeo completing tho formation of the 
circular disc inclined at 4f> B . Tho number of 
pockets in the rotor and stator differ by one 



Casing Lin 

Developed Section tliro Vanes 




U Hlinuld lii> noleil Dial, solid friction brakes, 
in noriH(!i[iiDii(!o of tho frictiounl rcsiBlnnco being 
practically constant over a wiilo rango of npccd, 
ofttmot bo success fully employed for tlio measure- 
ment of power generated liy a prime mover suoli an a 
petrol motor in ivhinli tlio 'torque n!n wmniiiH con- 
Hlant over (lio same rnngo of sjiccd, 

In Hiioh a enso it is extremely difficult to nmintnin 
tlio flpccd of tlio primo mover at o-vc,n nil npproxi- 
nmtcly constant vnlno, and the brake needs continu- 
OIIH attention if steady values of tlio power are to 
bo obtained. 

(iv.) The, Fraud* Water Rratx ' (fig. 0). -This 
brake in of the fluid friutimi typo and is veiy 
extensively uacd both commoroially and in the 
laboratory. It consists of a wheel or rotor 
attached to a driven shaft revolving inside a 
casing through which water is circulated. TJie 
casing is mounted on trunnions which enshroud 

," 5(01). 



on each side. Tho jiouhots between tjio rotor 
and casing tlnm form complete aimulnr olmnnIn 
of elliptical cross section divided into sectioiiif 
by tho vanea. Tboro is only a very umall 
oloara-neo between tho facca of tho rotor and 
tlio casing. 

Tlio formation of tho oliannols and vanes in 
shown in detail m tho developed Huet-imi of 
rotor and casing in Fig. i\, the section boiiifi 
mado by a cylinder, passing through the wftlor 
hobs sliowii in tho principal section. 

It will be scon that the vanes aro inclined 
at an angle of 4fl to the direction of motion, 
and that thotfo on opposite sides of the coiitro 
line aro at right angles to entili othor. 

Tho difToi'ontio in jiifcoh of tlio vnnoa wliioh 
may bo observed is duo to tho difforcnco in 
tho number of vanea in tlio rotor and casing 
respectively. 

If, in tho view shown, the rotor ho in*iv(l 
until one of its vanes comes into lino with ono 
of tho vanes oJ: tho easing, then the lino thus 



100 



DYNAMOMETERS 



tinned ]H ii fusion across n fiianml.fr of 1111 
approximately circular rtiad, ono Iiulf of which 
in fnrmnd by tho rotor mid llio oilier linlf by 
iho drtftiii^. The nmsnlurdiKd viewed along tho 
direction of motion has tlio elliptical apnenr- 
unco sIxHvn in r.ho prmmpft! sectional view. 

Wl iiyj Iho shaft i minted, mitnfiigal notion 
Hutu ii|i vurl-iiscH in Mm pockets in a plane fit 
lfj n hi tlio iixin, ti tut tho wiiisol niul <;aao are 
Mum nrgcil in nppiwito directions nltto at an 
alible of -liV', 

Tho oompononlf! of the forces produced arc 
Imlinifif'd in the divedtion [mnillcil to tlm shaft 
dim l,o llio ni-rangoiiKMit of (ho vanf's on 
oppusitn Bidofi of tho ctmtm lino, but i;tngcn- 
liiilly thuy react on the* wining. Tlio moment 
I'dfjuirdfi, tlumiforo, to prevent volution of tho 
RHHII is pqiiii.l to tho torque on (Jin shaft. Tho 
ivalor which in Hii|i|>liiiil (iontiniKiiiHly to tlio 
lmiti, whim I'litiiiing, jiaasos from pooluifc to 
(nidldil,, lit tlm ftiunn timti rolatiii),' at a high 
mid of Hpceul, linaJly oincr^ing ni a tomji^ruliiro 
H-liicili uiin lio I'Offiilnlisd ]>y tlio sii])ply vnlvo. 

'I'Jio hi'jiko in rogulatotl by moaiiH of tliin 
OL- ])lates, iiisortcd l)ot\veen tho 
orottwamleiiflins. TliorcMatancitj 
nfturud l>y tlio ln-ako :fiir a pni-iionhir dotting 
tiE thi! pluti^H varies apnroxinintcly ns tlio 
wjiiaru (i[ tlio Hunwl, HO tliat Ui liralco is well 
united For Uvting nmlor conditions of onnatiint 



and 



enso in puovidod with 
frbituJn wlioro tlm ohaft 
tbi'oiigli il, but tlio frkition of tlirao ronnta on 
tlio diinin^ und EH ineiiHiiral. Tlio OAHD In also 
]_ihividil with a tor([u arm supported by a 
H])rinpf lutbmco, Avliioh in turn IH HUHiiundci! 
from u liook wbioh omi 1m ndjiiHUid in a verlieul 
(iii'!<il,i(.n in orclov that tho lorquo urni lihjill 
riHituin Jiori/nntal. Tho load ifj hung lit tlio 
IMH! of tlm l,un|iio nnn dircdUy unilor (,ho 
Hpi'lrifi ItiilaiKK!, and the offodlivo torque load 
in (thlniunrl hy tnluii^ tlio diffot'otico of Hto load 
and tlm Hpijij^ Inilniuin reading. 

'I .'ho olTodt (*f tho Hhiico gatos in to rciluoo 
thn ufl'tuiUvo Hurfncu, llniH increasing tho rmigo 
<i fiprvi(i, T;h cajtauiLy of n dynamometer 
alifiiirbin^ WOO h*iuso-p(iwor at 80(J rovohilions 
a jnimilo nan bo adjimtfid tn absorb 40 horao- 
JHMVOV at 200 revolutions por minute. 

< v.) Hlr.t'.lrir.rtl 7Jmt(w. The National Physical 
.fMbnmtorij .Difnamomdcr, In tliin btulco tlio 
])uH f oi* dovolojjod in abs<ii'bed olcotriRally hut 
modiaiiionlly. Tho clcotrical incaa- 
of tlio povror dfiponds in Bonio mcaauro 
rm Uifi aiitiiininy of Hie instruments employed 
and on tho lumjiomtiii'tt of Urn field iimguot 
und iiniintiini wiTiilings of tlio gunumlm'. 

Tlid pffiiiti incivor iindor teat in ci>ii])lcd 
dirmtf, fn tJid rtFuift of a gnnoraUir, tho outor 
fniini! of M'hMi in moimiivl on lioni-ingH offoring 
nniall fi'i<iticinril nwiHlinmo, and the tortfiio on 
UIIH frarnn In incaHtirrd, The jiowoi 1 



is carried by vnry floxihlo ealilo.s to rosi^M' M* 
mafs by whioli it is dissipated us hont. 

J''iy, 7 shows tho mctliod of suppmrljnjf t-i 
fiold niagnot frnnio. Tlio latter it! ]i- ( ivi*l*' 
with hard steel rings A at dllii'i 1 oml, f.li*' 
rings lining ground truly (ionccntrio w itb *' 
JIXJR of the stlmft and scoiu-oly Jixcd to l-l 
Irani o. 

The rings rest on the soctora I!, H, whioli fH 
nlao <if hard steel ground truly cylindrical <> 
the curved Biirfnco with llio linifo cdj.;^ l 
centre. Tlio Rectors support tho \vlioto wcifil'i- * 
the goneraloi-, which being thus luoiintficl C!J 
oacillnto I'lii-ougJi a small arc with (x\i,riuini"l 
litf.le rcsista.neo to motion. 

Ball bearings mounted on vertical puwl.i J' 
jirovided at eneh end of tho gcnoratcu 1 fruit'* 
Ijcaring against tlio Bides of tlm Btixsl rini.(H * 
limit tho end motion nnd to talco tho Mii'ii 
should tlio frame inadvertently bo moved !< 
far in a longitudinal direction. 

Tlio frame is jirovided with 
torque- arms, ono on either side, 




. 

I /'W 



HO that the torque can bo measured when * 1m 
lirako in running in either dirtustinn. 

The torijiie arms aro balaiidud, innl oni* iu 
])i'ovidod in the usual maniipr witli nlopn in 
limit tho angle of oscillation. 

Tho load is hung from a knife edffo nn ottn 
of tho arms, a fine adjustment heJng obdiini-i I 
by means of a spring which partly rolinvfii 
tho load. It is in-ranged that oxtnumoiiH *F 
tho spring aro magnified and indhtiitrd 011 
a moving shoot of paper HO that tlio vnrintEi n in 
in toi(|uo of tho prime mover undor tiwl fir** 
rcooi'dcii . T.ho pa]ior moveinnnt in <>nV 
by a clock mechanism, and indluiitinnn 
Bpnotl firo also recorded electrically. 

Tho arrangement of tho recording iiiN 
nient is dourly ahown in the figuro. 

AH in the ease of tho Frondo waior 
tho hearing friction, and iimdim tally 
Jmish friction, is mcasiirod at tlio l 
arm, HO that the method affords an mui 
means of measuring power. It has tlm ilirt, 
dvantagos of having a small range of IIKIV*.) *, 
and speed, ami a heavy rotor, hufc theiio nt'tt 



-r I 
r>f 



DYNAMOMETERS 



101 



somewhat fsomponsaled for by the fact that 
UHI generator can In; used as a motor either 
for .starting a.n internal combustion engine or 
fur supplying power to n nifichiiic whoso 
torque remntaiie.e in required to bo measured. 

It is estimated that, under steady condition. 1 ) 
of running, determinations of torque can ho 
made on this dynamometer t( nn accuracy 
of 0-1 per cent. 

(vi.) Kilttj/'Ciirrent Brake (Vitj, 8). A very 
successful form of eddy -on went bmko has been 



The shaft IH partly relieved of tho weight nf 
tho frame by a liul; suspension attached In an 
ovDi'hoad Hpi'iTi^ balnuco, and Iliiw iTiclliod 
of suHpiiiifiioii emililes tho frame to \\c, .sup- 
jiortod without produdtig ft twintiu^ nioTiusnl 
about tlio slmft c!imlr. 

Tho overhung load on (be shaft can lio 
variect us desired by adjusting tlio tension of 
tlio mipport. 

'J'lio air gap hc-tweeii tlio cop]ior disea and 
(.ho field magnet poles m fixed, anil tho rigidity 




Section oti AB 



dvolo]]i!(l by .Dr. .1). K. Morris and 0. A, LiHtor, 
aTid_ SH deaerihed fully in a paper to tho .Bir- 
mingham Lm'.al Section of tho IiiBtilntion of 
.Klixslrieal IDngineorfl, 1005. 

Tlio briiko wan dcHigned to aliHorl) fi horso- 
powtu 1 at 1000 revolutions per niinnto, and 
inado for IIHO in tho Ulcotrieal Laboratory of 
tho [JnivorBity of Ilirmitifdiam. 

'I'ho ttppiinitna ia made for attachment 
to the shaft of tho prime- mover in phieo of tlio 
ordinary pulley, and coiiHwls of two cloniontH, 
ono in the form of copper discs fixed to and 
conooiitriu with tho Hhnft, nnd the other a 
circular frame also concentric with tho shnft 
nnd o any ing inagnetiHing coils nt regular 
intervals round its periphery. 

The magnet frame, or alator, is centred by 
a revolving bush neoui'ely keyed to the Hhnft 
and if* provided with a torque arm, jnolioy 
weight, nnd slops, in the usual manner. 

Two copper (Uses arc provided on the rotor, 
and are fixed to tho revolving bush ono on 
either sitlo of the' magnet coils, tho axes of 
whiuh are parallel to ^he nhaft axis, and by 
this nrrangemont both electrical symmetry 
and mechanical balance arc assured and the 
brake is rendered natatio. 



(if the construethui enables it to be made small. 


External yoke rings are provided nnd lire 


supported by brackets from the magnet frame, 


the braekots being clamped in mieh a manner 


that the external 




gaps between the 




yoke riiVgH and 






tho copper discs 




| IT 


can be adjusted. 




'--' 


Tho limit of 




i r 




tho capacity of 








t h o b r a k e i H 








determined by - 




z^i. 


? 


tho temperature 








of the magnet 








eoils. 




_. 


_ 


(vii.) 7*' an 








Drakes. The. 








Oentrifiiffal -fan 




(Fiy, 9). -Tho 




Centrifugal Fan y, (li tl _ 


Brake uaually 



consists of two square or rectangular platen 
hold by radial armu in siioh a manner that 
they are presented normally to the direction 
of motion. The bmko in more frequently imetl 
as a ready means of applying n load to a shaft 



.102 



DYNAMOMETERS 



rotating at n high Huncd Lhati an a immriH (if 
innn.Hiii'iiijr (.oi'nuo, .It m iiciscMHiuy that it 
Hlinulil Im eiiljUmlctl by means nf an aecsiimtcr 
dynamometer, I'ufc tho calibration iaaJYiKsted by 
vnrialioiiH in Icmiperatin'o and preHHiiro of Mio 
HiiiToumlmjr iitmoapliom, (.'roHU-diiiTcntM of air, 
antl Mm proximity nf supports, adjacent walls 
ii]|d lluor, mid (if tho primo movor niulor todt, 

'['ho loud in adjusted either by moving the* 
])la.(rs i tiling iho radial uriiiH or by iil.tiny platen 
of M. dilTorent HIM!, Uie.Hi) methods of adjii 
luiving llin ffrosit dimidvantiige of 
Mm Htoppitge nf tho pvinui mover under test. 

Atloinpl.H t.o rondor th blades adjustable 
tbirinj; mlntion hn.vc met wiih liltlo aiKsnp^a, 
owing oliiolly to tho ilifticnlty of designing the 
mi'.t'lifiimm hi oporafo agaiimt tlio 
fi>i'(:i i si (listing on ()w tiludra. 
Tim tin^jiid dito hi Ilio hhnlcx filonu, for 
(inliiuiiy H]ii',oilH itnil wi/:(^, vavius itH Mio Rqiuiri! 
nf tlin Hfiiidil, f.fio <!iilMJ of Mio riuliiiM of tho 
him I CM, Mm im?it. nf Mio Mitdc.H, Mio di.uiHil-y of 
Mm fluid in whicsli Mic [an is workiiif,', mid on a 
finitoi 1 ilopinuliiifr mi (,|io cnviroiiiiHiiit, 

r l'|-ni fun hralu) in oliini]) to munufatrturo and 
in iiHintlly DIIK.V l lit to Mio Hluift of tlio |)rinio 
innvor, Km 1 IJioso roaviima it in frequently 
UHiid niiinnuux'iiilly IIH n Imiko for " ruiiuing 
jn " ivinl "iimliimnmj" Itjats wluii'o (ho ^nnvcr 
\a not ro<|ui]'(!<l to bti Icnown with 
It iniiy 1)0 IIHW! for oompanitivo 
li!stfi prc>viiU;(l Mio (vtniospluu'iu oondi lions 
ami tin! (siiviroiiuHvnt roinuiii conatant Llirongli- 
out tlm U.'fitu, tint neglect of UICHO faiilord niny 
oil'csol; an uvvnr of 10 to 20 jicr uisnt in Uio 

llUHlHlll'Oll l()n[tl(1. 

(viii.) '/Vie " J$ticrtrgt)t " ./'Viu llt'ii !:r. for tenting 
Afii'tiiiuutiml Hiigiimx. In ordoi 1 to 
an fur IIH jioHHllilti l.lio cooling ijfl'(!(!t. 
on an Hiiroiuiul.-iiiiil oii^inc 'iindtM 1 llyin^ (Mindi- 
ti*!!!?!, it- iH I'HKdiifml Miat i\w tingiiid inidci' tent 
iiiinll work in a curn-nt. of uir projutilctl nn it 
jit IL Hj!od coin|)iii'nlj|(i wiMi tlm flying 
Tim iinnlinfr in tiiVcci|i!(l in tlm 

liy a fan hrako driven by tlui 
uiuliJi' t(^Li nnd inoitiifnd in a <ilunn!>(ir 

Unit of nn oi'diimry fun (!iiHiii(?. 
'J'lw inlrtlto nf tho air is in tlio milt; o tho 
onaiiif; oji|ii>niUi Uio fan (Mjntro, 

Hotiny < 11 ' mdiiil ongincH aro UHiiivlly mounted 
iiinid(> tho oHiiftrRiifc, ./''](/. 10, lioing tluwi in tho 
ifiniKt jinUi "f fcho iiKsoininf! iiurront of nit-. 
VIM) or voi'Liofil en/jiiioH aro fixed on a l>cd 
tho fan olininhor, and tho air from tho 
ts nrUUm is diroulcd u to tho ongino 
from iilioyo <r from tho front, 
fn UHI laLlor arriiiijiscinont tho fan is rti'ivon 
Mirnii/;f] nil nit^nodclinto Hhaft nnd iiiiivoi'aal 
iiiiitplin^i, 

.|i'ii' " niniiin/.; in " and " cndnranc'd " loatn 
tlio brtikci tuny lio (wililintloil by uicaiiH of nil 
iinilor, hut i.4 opon to tlio ohjtM-Liium 
luivo alrciuJy been miimnarini;<l under 



'- 1 *" 1 



fr 



KH, 



f 



t* 11 '' 
(!'*' 
(!'*' 



tho licading of tho "Kin Hrako," \f in - 
of j^i'oatoi 1 tiodHi'iioy it is usual to mmm'l 
engine on a floating tori|iie-ba!anc:B 
wbicli tlio reactivo torque on the <mjj;in 
bo iuenmirei.1. 

AVlieti tho engine is BO nionntctl it is ytiHcii *"* '' 
if accurato roBiilla aro to lio nhtaiii(;il t-li 11 ' 1 
tho nxis of tho roL'king franiu Hluill 
with tlm fan axis, oMirivisci tin; 
iiioiiwiired will diiTcr con m durably 
truo tori|iio according to iho 
fan in tho owsargot. 

;5 {.'!) TltANfiMISRlON JlVNAMOStK' 

,ii(ete.rfi.\t\ ca.soa wliero it IH 
keep a check on Mio jiowoi- <lovolo|K'<:l hy 
primo mover, or ivhoro tho absorption of ( 
power (lannoli convoniently he fift'ncitcd 
transmission dynamometer is cmployi-it. ' 'J^l 
inatrinnont exists in several forma of tui'Hl* " 
motoi'H, the function of M'liieh i-s to minimi 
the angle of twist in a Jongth of tho 
driven by the primo mover, and from 




li'lO. 10. 

measurement, by previous calibration or tty 
calculation, tho torque is deduced. 

(i.) llopkinson-yiiriwj Tornioiiine.tcr {/'Vf/. X I ) 
Thin instrument was designed by l.'rof I-.H MI i n- 
Uei'trmu llopkhiKon and Mr, Tlirin^ for (In- 
determination of tho power tnniHiniUt'd }ty 
turbine shafts, and iHitacd to a vory hu'^o cxli-n i 
on Hfoa in whips. The principle of tho appjmi (mi 
is tho measurement of tlio relativo anglt' * f 
twist botwcen adjadent seitfionH of ilm Hlimft 
and the indication of this movenumt nil n li >;< ^< 1 
senle, Tho length of the Hluift taken up !>y tlm 
instrimumt is very small, being, for my,on cj vtr 
H inches iliixmutor, about three diamottu'H It ir Hf^, 
and for Rtnallor ahafts about four diaiTictoi'M. 

The instrnmont ctinsista tiasontially of (.\vt 
flaiijfos clipped to tho sha-ft at a inonmirc'rl 
distance apart. A sleeve onoloHing tho ntnifl. 
connects tho two flanges, being formed iti]ji| 
with tlio one but froo to rotate tlirmi^K i 
small angle on tho other, by whkih \t in 
retained coneontric with tho shaft., Tho twin,), 
of tlio latter causes relative angular 
between the froo end of tho Hleovo iind 
flanjro adjacent to it, and this motion is int] i. 
oated on a fixed Hcalo by means of. a 



DYNAMOMETERS 



Tho mirror w mounted on tnmnioiiH working 
in bearings fixed to tho flange, the axis of the 
trunnioiiH being mil in 1. The mirror is pro- 
vided wifcli a short radius arm whidi is con- 
nected In on (i(ljuatul)lo block on the sleeve 
by a tliiti phosphor -bron/.o link. The tan- 
gential movement of tbo sleeve block ia 
governed hy n mioromoter screw in order tlmb 
tho relation between tho movement at the 
nulius of the mirror from t-lio centre of the 
shaft nml the spot of light on tiio scale may 
be ascertained, 

A lixed mirror is attached to one of the 
flanges, which is adjusted so that the spot of 

light reflected from it is rc- 
. ceivcd at the same -[mint on 

the scale as that from the 




li'W. 11. 

movable mirror when thoro is no tortjuo on 
the shaft. 

An nlcntrio lamp fixed just" above the scale 
provides tho beam of light which is reflected 
from the two mirrors on tho scale Hiiciccsaively 
na tho shaft rotates. 

A shift of tho apparatus relative to tho 
scale is indicated by an nltoration of tho 
position of the beam reflected hy tho fixed 
or " zero " mirror, nncl this nan readily bo 
adjusted by moving the snalo. 

Tho moving mirror is silvered both hack 
rand front HO that two rollootions, one on either 
iBido of tho Koro, aro roooived from it during 
one revolution of tho shaft. The mean of tlio 
two readings may thus ho takon whatever 
.the position of tho '/.oro. 

Tho instrument may bo calibrated directly 
,by applying a known torsion to the shaft 



of 



an iiifsrniitnininuti 



tirrtftit 




and noting the; reading of tho sumli 1 , ur hy 
calculation from a knowledge of the (omiuiml 
rigidity of tho shaft imtl tho various levoniKCM 
and distances involved in the conversion 
tho twist to tho movement of tho spot of li. 
on the scale. 

The apparatus gives 
reading of tho torsion in 
the shaft at a particular 
angular position in the 
revolution, tho angle 
being fixed by the posi- 
tions of the miiTom and 
scale, 

The torsion at a 113' 
other part of the revolu- 
tion may be obtained by 
mounting tho scale on a 
circular framoconccii trio 

with the shaft and shifting the scale and lamp 
to the angular position required. 

(ii.) The Ayrlon and Perry Toraionmctcr 
(Fig, 12). This dynamometer is designed for 
use in the place of Hie ordinary shaft coupling, 
which purpose it also serves. Tho two 
one on each shaft, are connected by 
of heslical springs, throe or four in nmuhiT, 
arranged in a position approximately dui- 
gonlia! to the shaft. When power in ti'inui- 
mittcd, tho drive is takon through Iho Hpriuijii 
which extend under tho load. Tho stroli-li 
of tho springs allows relative angular move- 
ment between the shafts, and this is iiidieutnl 
hy a lover arrangement which has the nltiminh 
oiYoet of reducing tho distaneo of n 
bead fro in tho filmft 
centre, The radial 
position of tho 
bead is observed 
against a hlaok 
disc on which a 
Hoalo is marked. 

Tho apparatus 
is calibrated di- 
rectly or by cal- 
culation from the 
stiffness of tho 
springs and tho 
magnification of 
their extension 
which has "been 
employed. Cali- 
bration against an JI'KI. us, 
absorption dyna- 
mometer is preferable if it ia thought Chat. 
tho arrangement of tho springs adopted in 
lilroly to givo different calibrations statically 
and dynamically. 

(4) TrioRNvciioiT onFnounE Brnvr JlvNA- 
MOMETi<:R 1 -~Tho arrangement of this tnuistniin- 
slon dynamometer is shown in Piff, 13. Tint 
pulley T), fixed to tho shaft of the prime mover, 
drives tho pulley F by moans of a bolt which 




101: 



.DYNAMOMETERS 



in In ni round tin 1 , two puthys A ami H. 
Tho luttor are uupjioilcjd by a frame AHL 
which i.-t pivoted at I'!. [1, is obvioim Unit the 
downward f'U'en (in tin; piilloy A will exwed 
that on tlm pulley B by twk:o the liifl'oronco 
in toimioim of the tight mid ntadi sides of tlio 
holt on oithor tho driving or driven jiulloy. 
Tlio fmiim AISL will (lion* fore Lilt down- 
wiu-dn ut A, lint tls Hymmetrkid position is 
rcrttiirod oilhor liy a forco at .!.', or by lidding 
weights to 11 niello-pan filing 011 1111 extension 
of tlio nrm A I! at \i. Tito motion of this ond 
of Mm lover is uonlliHxl within amnil limits 

l>y Itnmnrt llf HtopH. 

Tho holt lonsion difl'et'muso in oppressed by 
'.rIVi/^ft uml the horao-niiwor developed by 
|[.l'. = aB-TEtN/fifiO, whoro K uml N' are the 
nidhift in fiMil and speed in revolutions per 
Heeond I'e.speelivcly of tlio dnvoei pulley. 

Tlio powor in not tuanHinittod entirely 
witlnmt IO.I.H liocaiiHo of tlio ulip of tins belt 
and lb<i pulloy hearing I'riulion. These IOHHCS, 
hmt'iivcr, oiin bo de(t:nnined by independent 
dyimmomolw toilsi. 

g (fi) DVNAMOJIKTKII OARS AND TttAOTIOM 
J)VHAiMoMBTl-:n.H. Many itiBtnniHints lin-ve 
ImiMi ili|-iH!il Lo HKtriHuro tlio roaiHtnneo of 
vohidt'H to tniolioii nixl u!sn Hut tniotivooirurt 
of mi|f-|'o|K)llil vohiolcs. '.I'liu }mll ta usually 
tL'tiiiHinitluil llii'iniffh oifchor Jt Hinnll pluiifj-or 
or (liibplitugirt, in wliiuh antui I3io jH'e-'isiu-o sot 
up in a ]ii|iiid column in recorded by nicatiH 
of it prosiHuro j^ango, or through lioliciil or 
lainiiiiUeil spvingH tho dofLoution of which IH 
indicated on a soitlo. 

(i.) The. Jtrilish AntuH',i<tlitHi . Apjiiinttus, 
KOIILO nf tlio cfti'lionb IC;H(,H in Uiia country 
ivoro <unTid out witli a Hjiocinl dynaniomotor, 
iloHimusd Cor tint Ih'itJHli AnHooiution, for tho 
inimHiii'tiiiioiit of (.ho rosmtuiKio of road vcliiolca 
to triiotifni. 1 

Tint iippnnitim (tonipi'inod n cnstor fin mo in 
wliioh roiild ]>(i iiiinmU'd a Hin/rlo wheel on 
whiuli tlm ox])(M'iino]itH wisrn to l)u innclo, a 
of IOVCI'H for tntHHtnittin^ to a miuvll 
1 tlio pull oxisftod on UHI whtiol, a 
roHHiiro H |I11 M" f*"* n^iHtm'ing the 
pull, niwl a rciiimling Hpewloitiotur. 

'.I'liti finntor frames WUH of wt'ou^ht inm aiul 
r in slmpo, ami was iulii.|i(:wT to take 
of viu'ioiiH widOiM. Tho axb of the 
oxpori mon tut whtiol was tnoiintccl on 8|)rings, 
OHO undiM' oah nido of tlio fnimn. Tho Hpriugs 
imiwl wcro o( tho ui-diimry luniinated oarriago 
typo (lOHHt-ninlwl in Hinsh a rmmnor that 
lilioii 1 fttiO'npHH floitl(3 bo n<lj ustpd by varying 
tho niinihor of plulcs Conning a spring. Tho 
fnuno WUH li/ul(!<I by liiiHt-iron weights fitting 
over |.|K> (timtor frintin. 

An iiH.ai'f H in*nl. \vtw mndo to tlm lovers 
U'11-nHinittinj.f fclni- pull Fiy a sivivol jojnt whiuli 
allowed tlio fi-ftiiio to oHcilliil'o vortioilly and 
1 ItrlLirtli ABHoeliil.lon .lt(!j(iii'(, JU02, 



*t 



I ' 
'* 



to follow froiily round a, inirvo withoiit ailo*'- 1 ' * * J " 
l.lii) rouorclH, but HO hold il, (.but Mio ^ r h*" l<f 
alwiiys roiiiaiiic-'il vcrtitml. This fnb-i'iiiu ' '^ 
tin; luvor uoiikl bo inovod to oitlioj- ,,f i't H r 
liosifciona aiiuh that tho presHiin) 011 Llio pliJii^*' 1 ' 
was ofjiial to, or two, four, oj> oif^ht tim,.}! I I* 1 ' 
l)iill cxt)rf.(!(l on the franio. r j'h i'anuo nf ' '*" 
apjiaralus could thus be vtiriisd from j"i to/i(l(> ' ' Jfl ' 

The I'ouord of ])rossuro and HJIPIH! WI\H TI'>* '" 
by pomuls on a sheet of jMiijer which \vu* ( 
rotated by a roller tho motion of which \vn' sl 
obLained through gearing from tin; mail \vli'<'l- 

(ii.) The, Jli/ttll lnatrmnv.nl. Tliin 
niotci-hiis IKSCII specially doMignod for (,], t \{ 
inination of the draw-bai 1 pull of du-m [,\-mi t 
and the tnietivo I'osiHlanuo of ploughs ^voi'l^ i 
under various conditions, 

The pull in transmitted from tho lmc.|.ir 
the ])longh through a link or oliain an* I 
piston working in a cylinder. Tho litlt*'!" 
eontaiiiH, a rubber bag containing liijuki wlii' 7 ' 1 
is comjiressetl by the piston. Thin timi^u '*' 
unit is hitched in one of tlmio dilTornnl, WJi.v" 
giving different ratios between Iho fiull INK I lii" 
presHiiro on tho rubber hag. The tlux-e hi^'li' "' 
corninpoiul to maxiinuin pulls of ;{()(!, UOl), n n' 
J200 Ibs. res]ict!tiv(3ly. 

The rncorilor consists of a llriHtol i-(iun J ii*jt 
prcssnro gauj^e. It is RonnecUid tn Lbo ]n- ( 'HHin'** 
unit by a flexible inotulHti tnbn wliidh !OIIV<\\'FI 
the liquid inn tor presHiire from tho inhhcr 1 HIJI; 
to a .Bourdon pressure tube whioh aoUifil *"' 
the pen meehanisui. A neodlo valve, inwft I 
in tho |)t-eHsure tube, may he adjimled Lo ooiil i 1 * ! 
the How of liquid and to damp out oxorjiHi vi- 
vibrations of tho pen. 

The chart is a circular Hbeet of papur divii ii'rj 
hy a Briesof ciuicentrio oinshsH aerimii whifsli <-l i* 
jicn travcld in an approximately nwHnl ilin-ot i< i i 
from tho centre outwardH with incinviwiiig j 1 1 1 1 1 . 

The chart is caused to rotate by a wlii-i-l 
which rolls over the ground and wfiieh i'i 
connotitod to the recording hn-iiruiiH'iit 1*,%" 
a flexible dhaft and miitablo gearing. 'TIii* 
carouniforonoo of the chart im divided itt1*i 
equal ]wrta ouch representing n diiil-ai i*-i* 
travelled of 100 feet. 

A Hccond pen records tho nla]Jff<l [Jinn itii 
an annular space at tlio edgo of (ho oliiir-l. 
A clock in tho recorder cam.', titled will* n, 
cam, trips tho time penal ono-miimto inlorwi In, 
inul fraotioiiH of a ininuto may bo (wtimu.li'i| 
by counting the number of smaller |nu' n<v>i 
which the jion liaa travelled. Tlnf diviniim in 
nceomjilishcd by dividing tho annular tt]i;iic<i< 
by a number of conceutrio ciixsltiH and 1 ty 
caiihing the time pen to trnvol from Uir on ( *-r 
to tho inner ring in tho mimito inturvul, itf tt-r 
which it is aga-in tripod baelc to tlio outt^i 
J'ing, its path being praoticnlly a radinl lisin. 

The recorder is lightly built mid in i>nivi(l r], 
with straps by which it is oarrind ly 
asHistant during a test. It if) urrnngud 



DYNAMOMETERS 



lOfi 



the rolling wheel may cither bo clipped to the 
tractor or guided by hnml. 

.Kmm tho chart obtained, tho draw-bar pull, 
tlio (Jistuticn tru veiled every nix seconds, and 
the speed during tlio test mny ho deduced. 

(Hi.) Tim National Physical Laboratory Tractor 
Dynamometer Car. This apparatus was con- 
slrneted solely for measuring and recording 
the tractive effort of farm tractors, for which 
purpose it has hecn successfully used. Tho 
ear employed was a heavy four-wheeled lorry 
trailer, tho roar wheels of which wero fitted 
with spends and band brakes, tho latter being 
operated by a hand wheel from the front of 
tho vehicle. Tho apparatus was mounted on 
au extension of the bogie frame carrying tho 
wheels o the- trailer. 

Tho pull of fcho tractor was converted to 
pressure on a leather diaphragm by moans 
of a bell-crank lever suitably pivoted, tlio 
diaphragm being faced on the pressure aide 
with n, rubber disc to prevent loakngo of the 
liquid in the dia])hi'agm box through tlio leather. 
A flexible hydraulic pipes competed the dia- 
phragm easing, to a JJourdon pressure tube 
operating a pen mechanism, and a record of 
tho prcNsurc wan tlmn obtained on a roll of 
paper. The latter was caused to move pi'o- 
porti imally to the distance travelled by the 
our, tlio driving drum being rotated by moans 
of gearing and a floxihlo abaft from tho 
loading road wheels. 

Two other pens wore also provided, 'one 
operated by a, clock in order to give time 
indications evory two seconds, and tho other 
operated through gearing and giving indications 
of tho revolutions of tho tractor ongino. 

Tho diaphragm 'box, to which was attauhed 
the fulcrum of" the hell-crank lover, coiikl bo 
adjusted vertically so that tho ropo or chain 
eomiflL'tion to tho tractor could bo arranged 
hori/ion tally. 

Jn currying out a tost, tho brakes of tho 
car wore adjusted, and the ear loaded with 
dead weights, until citlior tho engine of the 
tractor WAS pulled up or tho driving wheels 
began to slip. Thus the maximum pull of 
the tractor on tlui piirtionlar surface chosen 
for the tests was obtained, 

(iv.) Railway Dynamometer Cam. Dynamo- 
motel- cars have been constructed for traction 
testa nn locomotive engines and tractive resist- 
ance tests on railway rolling stock. Tho oar 
uwnally takes tho form of a special coach, tho 
draw-bar pull rind buffer thrust being recorded, 
with tho speed, on a paper-covered drum driven 
through gearing from one of the road wheels. 

A most successful car of thin typo is that 
designed by Mr. George Hughes for the 
Lancashire- and Yorkshire Railway Company. 
Tho various instruments with which this car 
is fitted finable complete records nf the per- 
formance of tho locomotive to be taken, 



including draw-bur pull (or pnuli) uprcd, 
acceleration or retardation, JUH! boiler invwuiirn 
of this locomotive'. 

Other factors hilliienuing (lie performaiirii 
arc also indicated on Hit* e.lmrt by oliMsrvern. 

Considerable care nnd experience is n-ijitiicil 
in the design of a car of this kind, and the mmo 
salient features of this Lancashire- itml Vnrk- 
shiro ISaihvAj' car are lieie Hosortbed for I lie 
first time by tho courtesy of tho (.'liicf 
Engineer of that Company, 

(v.) The. Luncftshirc ami Yorkshire Jlitiliwy 
Company's Dytiaiuoutcter Car. The dnni'-liui 1 
pull and the thrust on tho ]>ull'i)i nf thu cur 
lire transmitted to two compound npringM, niii> 
being provided for the pull and tho other Cm 
tho push. Each is made up of a numhur nf 
independent plates bound together by a pair 
of buckles at tho centre and cxiimocilod hy 
links at the ends. The link pins can lio with- 
drawn separately as desired, and this wialilm 
tho mi mber of plates in opemtioi i to hn 
adjusted to suit the load hauled, from a niiij'1* 1 
coacli to tho heaviest train, utilising tint full 
deflection of the springs. 

Tim spring deflection JH recorded diri'otly 
on the record paper without tho inlorvoiitiun 
(if levora, showing draw-bar pull nbove, \\i\\\ 
buffer thrust bislow, a datum lints. 

Tin; external enrriago coupling arrangement 
aro iitandard practice HO that (lit! oar ran 1' 
coupled ii]) an readily as* any other vchinlr. 

Tbo draw-bar and buITers arc oniinec.ti'd In PI 
rigid frame which moves eaeh net of Hjirinn" in 
0110 direction only so that the tightness of line 
screw shackle between Hid ongino and Mif cm 
does not affect tlioir indications, 

A c<inipenHating beam wjualitiC's tho llirtml 
on thfs buffcrfi -when ncg<itiaiing a ourvo. 

Tho draw-bar passes through a f rktifni dnvii'c 
which can bo brought into operation to (.alt it Un- 
load off the springs when tcslH aro not lieirju 
made. The device is also used to abHorb exrcp- 
timitil shooliN during the last inch of defli'i'limi 
of the springs, Amain cross-beam ni-ur |ln< 
centre of the eav imder-fninio forms a t'nnndu 
tion for the springs mid the Jn.'iliiinieiiL luMi-. 

Tho motion of tins ear is not recorded Ei 1 

tho ordinary road wheels but from n ujK'Hnl 
n^oaauring wheel arrangiid between tho lending 
ami trailing wheels of the bogie, so that llii-ie ii 
little lateral moveniont when round iny ciin'i-M, 
Tho measuring wheel is ])ressed ou tln< mil by 
a spring and can be rained or lowi-red n't 
reriuired. Tlio motion IH transmitU'd to ili<* 
instrument table by worm gearing and Jlcxibb' 
couplings forming a positive cb'ivo. 

Tho instrumont table curries tho 1'ci'nnl 
papor drums, the speed gear which rctfidnli-x 
tho relative speeds of the po-por and the train, 
a distance indicator, a work mtogmliH 1 , n 
recording and a visual spcodknnotor, a ntinnlnnl 
electrical oloclt, nnd an inertia ergo]Ue(t)i', 



100 



DYNAMOMETERS 



Tho record parior nan In; driven afc speeds 
varying from six inches to twenty foot pur 
mile, travelled ; a countor marks llic paper 
every mile. 

'[.'ho work integrator consists of a dise 
rotated from tlio roiid wheel, and across tlui 
faco of tho diso n roller in moved by tho 
extensions of tho springs. 'Kim rotation of 
tho roller fs therefore proportional to Urn 
product of llio di'itw-biir jiull and the distance 
traveller I, and this wwkisiiontmmwsly recorded 
on Urn chart as a serrated diagram, each peak 
represent ing approximutely f)l) horae -power 



velocity (aiKH^Iei'ation nr rotunliition). '.l.'ho 
inli.'gmtinjf I'cilltsr multiplies tliis furuo by 
distatioo and tlic result in indicated on tlio 
record ]>ai)er i\a an inclined lino. Tins change 
in tlio nrdimi-to of this lino roiireaonts tho 
ehiingo in tho algebraic sum o tho poltsntial 
ami kinetic energy j)cr unit muss of tlio train. 
When coasting ft'oo, tho loss of oncrgy recorded 
is duo to train resistance, and is tliorcforo a 
dii'CGt indication of it. 

.liy means of a run niado up of alternate 
haulinya ami coastings tho ei'gomotcir pi'ovides 
data from which tho work {.lone by tho jirimo 




Fio. H. 



minutes per \it\\r of springs in USD. A conntor 
gives llio tulal positive, total negative, or 
algobraio sum oE tho horse-power minutes 
clone by tlio draw-bar, as required. 

The speed recorder works on a positive 
principle, namely, that tho distnnoo travelled 
in a definite lime (4 scca.) gives a measure of 
the moan speed during tho four seconds. 

(vi.) The, Inerliit Urgomeler, - This was 
introduced by Joseph Doyen, Ohiof Engineer 
of tho Belgian State KnihvayB, and is a com- 
binntion of the Dcsdmiila Inertia dynamometer 
(ponduliiin) ami tho Atlhanh-AbakanowicK in- 
tegrating mlloi 1 . Tho pendulum is mounted on 
knifo edges mid swings in tho direction of 
motion of tho cur. Tlio tangent of tho angle of 
the pondnhim with its neutral position is pro- 
portioiml to the algebraic sum of tho forco 
o gravity and tho forco producing change of 



mover can bo calculated. By combining thin 
information with that of tho draw-bar integra- 
tor llio locomotive resistance, train roHislnnec, 
total resistance, and acoelerativo off out of the 
locomotive can be obtained for any speed. 

Curvature of tho track is indicated and hns 
been found to account for many peculiarities 
ill tho diagrams obtained. Fig. 14 is a general 
view of tho instrument table. Tho work 
integrator is shown in the centre foreground ; 
tho lover from tho draw-bar springs stands up 
through the, central slot in tho table and tho 
pendulum lover through, tho slot on tho left. 
Tho orgomcter drum can bo soon to tho loft 
of tho top of tho draw-bar lover. The clock 
is removed to oxposo tiio orgumotor to View. 

Jfiff, 1C is a specimen, reduced in size, of 
tho chart obtained for a run of approximately 
six miles. 



DYNAMOMETERS 



107 




108 



DYNAMOMETERS 



(vii.) Tilt. ,S'W,s'.v tit<tl,>. fltiilic/tr/ f.'ai: Much 
ol' tho ii|i|>;M'iitiiH liUi'd in HUM dynaiiioiimtai- 
iiar in in ninny iu-;|>i>f!tn similar h that of Uui 
mid Yorkshire Kiiilu'ay (,'ompany'H 
., 'I'lio prin.iipal dilVoroniio heUvoeu 
tlm two C?UM lien in tho inn (hoi I of monHiimii* 
llio trjtdtivo oll'oi 1 !., whidi in tlio [>rosi3iit 
EriHtiiimi in liy (ho IIHO of hydnmlit; gear, 
Umloulilcdly Mm hydraulit! dynumnmetw lias 
disliimfc jidwmtiigcH over tho priii! type, 
pmvidnil it is (.'fitfully deigned and acoimitoly 
inado. 

Tho ]>nll of (ho dni\v-lmr in tra.nmuitti.id to a, 
Htiso! |iliiiigcr working in a stool eyliador, both 
uluinoiil.H hi'ing ground so acmimitoly an tn 
render tlio nun of packing nnimi^fwiuy, Tlio 
cylimlor in filled with oil hy which tho pressure) 
in trniKuisitted (o Mm rmjrdinj* instrument,, 
uiiil it in iimmed that tHiBro ist a vta-y slow 
l<;il[ of oil !)it(i\v(!Dii tlio pliiiigni 1 IUH! tlie uylinder 



A cfililiratud holicul Hjti-iny in fitted In'l.-^' 1 "* "'! 
tlio two dill'nreut.ml plungors and \K (.inijii'*'-'- 51 ''*" 
by tln!ir motion. Tlio (ioinjimsHiun nl" ''"' 
Hpfing is a nnjiiHura of tho I'i'Midljtnt. end J"^ 1 '*' 111 
on Iho i)hingoi'ri and, thoi-cforo, of llm dilV^i 1 ''* 1 *' 1 ' 
hehvocti the draw-bur pidl and i>i]|}' t . r l.lii 1 !'^' 1 
and this motion IH traiiHformd dircetly '' ' '"' 
rcooi'd |)ai>or by a rod carrying a H(.\-|O. 

During prolonged nms tlio nl<i\v \m I* t^t'-*' 
past tlio main plungers may emiHii oiin of l-h*' 111 
t<i toiioli the base of H (syliinJoi-, !,,,(, ' 

sued a condition ran arise an ecjiudirtin^ 
i.s brought into operation whidi lias tho 
of cqutilisiii/j; the prosanrra in thn l,\\ r o oylin'-l 
and restoring thoir central pnsitionN ns H! n * 
in tho figures. Fresh oil is dnnvn itite* 
cylinders from a rcaervoir, Lhrnujrii a ii 
return valvo, whon required. 

g((i)Sra]iAT, BYJTAMOSIKTKKS. (i.) '['If. Jta 
hr Lanchestc-r Woi-tti-r/eor Teatin^ &lnrliinf 



v** 




wall in inxUir to iirnvMo liil)i'i(!ftt.iti for tlio 

fiinnoi'nml In niininiiMit it.s friistitinal rostHtuncjo. 

r [.'lio iiei'iiiiffoinmit of tins III-CHSHCO imiL io 

HllOWIl 111 /.'/y. t(j. 'I'lllllX! ui'll tiro f)lltHjT ( . rfl) 

iiidiimt^d at A and II, lilting into cylinders 
wlihili arn ntaciuil liacl; to bade unrl fonnod in 
a Hulid foi'^hiM. Tlm ilraw-l)iir pull in imiiH- 
niiltcil d> oiui of tlm |>luiifj((r3, nnd Llio Inifl'or 
Uiriuit to Mm oilier, liy imsiina of Lho miNHlioa<lH 
C! and I) and Mio roiln 10 and K. The Itithir a-rq 
. mndtiil hy rollora nuitnlily HH|)inirt(!d by a 
1'jgid fmino. Tlm clourfinco wpawH in tho 
(tylindoi-fl, Imhiiid tlm nlungera, am ooiinccted 
by |i|>i>H to ii diHtrilnitinjf valvo, and from 
tlmtiiid tn Kin rouinxling inoohanifuii. 

Thn vvwm\i\r consiBts of two sinall inofiHuring 
nyliiiildi'H iirnuigod in tandoin and provided 
u-il.li (lid'onviLiiil ] iluiijiorn ])|H)f'd tu ouch 
ol.Jmr. Thin iLft'iiiiftt'-nuiiit ]H'ovid(!S that liy a 
jinifuliln ,in(,|,i(ig of Mic distributor valvo tlio 
miiillmil, ni-t-ji. of (.(u* filuiiHof'H cxposied to Iho 
oil prcHnuri) from (lin main nyltndor.H iiuty Jin 
variitd in tbr nilio of I ; 2 : ,"! r ' Uinn by rolation 
(if thn (liHtribiitinK vulvo it is jjrnisilijn (<> solccsfc 
ottliiu 1 of thivn Hiialos for roudnltng Hit) load. 



' v<1 

t '*'* 
'' 1 rl 
1V ' ' 
<!><' 

" J ' 
"* 



by Jlr. X \V. JjnKsli*'*^ ''' 
for Mm aticiinito incaMii *'*" - 
mont of tlm (iflioioiu^v * '^ 
worm -gen ring. A *t 1 1'*- 
grammatio Hltntfili af iJn- 
a|)[iaratu.s ia givci ri in 
Jfiij. 17. 

Tlio iiHUHmioy of nni I*-* 1 *" 
worm gt'iiT's An' j 1 1 1 ^ v ' *' 
tninsiniHsion in of 1 1m t r* U'i' 
of ilfi per limit, and, uii*l'i' 
the licnt eonditioitniif t.nn I 
ingamHuliriiiiition.iiM Ii ip'li 
as 97 pnr font. Wtlli m ir'li 
ofiicioniiioH, He])aniln il<* * 
minatioiiH of Ihn tiir-tf*!*-!! 
in tho worm mid ii'oi'rii- 
wlieol sliafts l>y any of tlio inothndH idr'jirJy 
deseribod would bo liable (o giv mmln]i.rlini* 
rcsulta unloss the awinnioy nf thn im-amm-) 1 1 1 1 4 
in oauh IWF;O was within a ftmall JYmtlion * >f t 
jior cent, of the trno valuo. .Kor oxamjit* , in 
the ca.so of a goal 1 of 07 per eont cHidi'm^v, i f 
the torques nmild bo measured Knpiu'alfl^y 1> 
an aec.nnifly of 0-2 per cent, tins <xx|mrimi ri * n I 
dotorminationa of the olncionoy might iviii;><^ 
from 80-fl to 97-4 par cent. '.It in oviil<*til . 
therefore, that tho ordinary mothodn of 1m-* [ iit> 
measurement in which tho orror may lio u n 
much an 2 per cent are quitn nslot!s for t )M> 
purpOHO, and that a method of inuuli gr^n 1 or 
accuracy is required. Tho Lanehostor imi(^li i i it< 
measures, in cffcut, tho ratio of Mm t\\, . 
torques, and the over-all ofliuionoy of a vv< >j-n i 
gear with its hearings can bn ohtuinrd wiiti ij| 
an accuracy of O2 per cent. .Indeed, dirfor<'iif,j, 
of efficionoy duo to snob oaiistiw as olitm^j in 
tho tomporatitre of tho lubricant <!im Iio 
detected. 

Ji of erring to Fit/, 17, the gear box M 
ported in a cradlo A in -such a niannoi 1 tliu-l, J (. 
lias freedom of motion through a small 



DYNAMOMETERS 



10!) 



ulioiit two axes at right angles, The worm is 
driven by n sluift .15 through the intermediate 
nhfift (', the latter being provided with uni- 
versal couplings nt each end. In tlie same 
manner the wheel shaft is connected to (.he 
bevel box .K through the shaft D and fhe 
universal couplings KK Tho load is sup- 
ported by a bracket .K fixed in tin; arm 0, 
the axis of tho iinn being parallel to, and in 
tho same vertical piano us, the worm-shaft 
ax in. 

Tim load is not fixed directly to the bracket 
but is carried by a slider from which it is 
hung : by n screw and nut device tho distance 
of tlie loud from tho axis 
of tlto arm eau be varied. 

The position of the 
bracket with respect to 
tho wheel axis being fixed, 
tho moment of tho load 
about that axis is equal 
to the product of the 
weight and the length of 
tho arm, and is always 
the same for tho same 
load. 

Tho moment about the 
worm axis, however, can 
he adjusted by means of 
tho screw gear, the rend- 
ing of the scale on the 
braeket giving 
taneo of the 
weight from 
the axis. 

It will bo 
Bonn, tliore- 
fore, that 
assuming the 
gear efficiency 
us 100 per 
cent, mid the 
gear ratio as 

It., the speed of (,ho worm being K times that 
of the wheel, the tin-quo on tho worm shaft 
will ho 1/K timoH tho torque on tho when] 
shaft. Tho load being tho sumo fm 1 each 
torque, tlie distance of the weight from the 
worm axis will be 1/1.1 times its distance from 
tlio wheel axiN. 

Tho efficiency of the gear being less than 
100 per cent, the load must bo moved farther 
from tho axis of tho worm in order to balance 
tho gear box against the two torques when 
running undor.load. 

The calculated distance of tho weight 
from the worm axis, assuming 100 per cent 
efficiency, divided by the distance required to 
produce a balance, gives tho oflioieney of tlie 
gear. 

Tho drive from tho worm wlieol is taken 
through tho hovel box to tho belt pulley M, 
tho latter being of such a diameter that it 




tends to drive tlio pulley N on .the driving 
shaft ]i at about 5 per cent higher speed 
than ia established liy the bevel and worm 
gears. 

In other words, it is arranged that tho peri- 
pheral speed of the pulley JM IH fi per cent 
higher than that of the pulley -^i 1 - 

Tho belt connecting (bo two pulleys can ho 
adjusted in tension, over a wide range, an 
increase in the tension producing nn increase 
in tho torque. Ily this means the pre.ssure 
between the teeth of the worm and wheel 
can be made 1o correspond \vtlh Uie trutiH- 
missioii through the box of as nmcli as ISO 
Uorso-pmver, it being only 
necessary to mipply the 
loss of pnwcr in tlie gear 
and iippfiratus from an 
external source developing 
about 15 bor.se - ]iowcr. 
Tins ingenious principle 
enables prolonged tests to 
bn carried out at a wmall 
fraction of the cost which 
would ho involved if 'the 
whole pmver were devel- 
oped and absorbed. 

(ii.) iS'/jiu' (if.tr)' und Driv~ 
jiff/ (Uitiin- 'I'p-tlijifi Miif.liinc 
(National I'Hysiini! Laliuiu- 
tory}. This inticluiie is 
to mciiHiiro tho 
(Jifl'erotiec uf 
the torques 
of two sbiiftH, 
together with 
tli mcfifiiins- 
menl of one 
of the torque.'! 
sopaniteEy. 

It will b 
evident that 
the high do- 



Via. 17. 



gi'co of accuracy rcf[iiircd in llm 
machine is not essential in tho 
machine. 

ThiiB, supposing tho true eftioii'iioy of 
spur gear or chain drive in i)7 jii'-i' wilt, 
and that tho determinjitJoiiH of tli<* torqui) 
and torqno cliffi'rcnen am eaeli witliin 2-5 
]ier cent of (heir into values, tlie esti- 
mated value of tho efliciency 'f l-lie trnn- 
mifision from tlio ohHorvatioiiH may rnngo 
from !)((<) ])er cent to i)7-l ]ier cent, whidi 
IH of a higber degree of ncoiivnoy than 
that obtained by mrasui'lng llm icirquo ratio 
to 0'2 per cent, 

Fi(j, liSahowHthearrangomontof thn nuiohino, 
Tho frame carrying tho gears in onUroly sup- 
ported by horizontal I;nifo edges, and both 
driving and driven shafts are considerably 
extended and provided with ball-bearing uni- 
versal joints at each end, iHcinjv supported in 



110 



DYNAMOMETERS 



this manner, the frame can execute Hinall oscil- 
lations in 11 vert'iriil plant! tilxmt its neutral 
position. 

Tho intermediate wheel is rendered neces- 
sary in oi'dtsr to soeum Unit the reaction on 
tlio fnime Hhould bo equal to the difference 
bet\vcn tlio torques of the driving and driven 
shafts, and for this to lie the fins* it is requisite 
that tlio shafts should rotate in the stuno 
direction. 

Tlio lirst and intermediate gears mid tlio 




Tilting: Frame 
Arrmitfeil furClmin Drive 




Tilting Frame 
Arrnngcd for Spur Gents 




intermediate and tlio third gears form two 
pairs under tost. 

When a chain drive ia under teat no inter- 
mediate gear is necessary for tlio shafts to 
rotate in the same direction. 

If no in tor mediate wheel wove used in 
the gear test, tlio reaction on the frame 
would bo equal to the mim of tlio torques 
of tlio tivo shafts, and the object which it 
IitiH boon attempted to achiovo would bo 
defeated, 

Tlio frame in provided with an oil dnsh-pot 
fur damping its oHeilliitions and a torqiie- 
ann sonlo-pan and spring for tbo torque 
difference- measurement. Rigid stops nro 



provided for (lie torijiir mm ' 
amplitude, readings being );il>i'ii * 
in lovel. 

A J-lonkmsnn-ThriiiK Inniii'iin'* 
to detormino the l.ort]im <>n llm '' 
and in carrying out a \<-n\ mi *i' f 
lutes tiio torquo and nminluiim H J J - 
value, whilst a second ubr,i>nrr 
with Lho torquo imMimirnnrrM i-*i 
frame. 

Tlio method of iii<irra:>im: * ' 
between the gear lunth in n i|i* 
oiplo as that adoplcd in MM- 
mtxehinc. This SCCIII-CH Ibul i.nlv' 
power needs to bo Hiipiilli il fi.m" 
source. The centro ilisffini-n n( tH" 
la made adjustable ovor a \\i-l 
aeeominoduto varying ni/m .if 
kmgtlin of chain drive. 

])uring testing tbo tiltim; fi:mi 
onoloscvl in a light WIHH and \>\\ t* 1 
to spray tlio lubricant on lln< *:' 
being supplied by mean!) of i\ Id' 1 * 
mioh n manner that no ronlml mi 
exerted. 

In testing spur goai'H llm vitliif 
T a on the hist gear nan ivfidih I 
from the observed (laid. 'I h * 
of a pair of gears in |(ivrn, 1 1* 1 

t}= X/Tji/Tj, whoro T, in (h<< im-n 

tlio driving shaft, 

Thoofficionoy of aeliain In ph. n H 

(n'i.) ft pur flf.ar-hiu: Ti-iint^, 
(Nafional Physieal Ijiilmi'iilm v), / 
(bis machine tbo gear liu\ in nn.iti 
a manner that it is free lo <>".< iM t 
moan jiosition on tbo iixitt nf lli" >lt 
and the torquo on tlut frnnic "I t I 
is balanced and meaHuri'd. 'I li" i 
only bo lined in onsen \vhi'it> lt t > > 
driven shafts of tbo unit m.-- ^ 
Icavo Hie box at o|)]mml" < i 1 
usually tbo form of gear \i--\i - -> 
mobiles for winch thu appitmhi't u s i 
designed. 

The unit under tost in fhctl In st, 
frame provided with hnlluu i *i 
axially with the main Hliuftn, Tdi 
arc supported in biill-bcaiini- 1 r---. 
frame and gear box ean till in i iftu 
tbo frame being littod \vilh n I 
provided with the usual da!i|i.j^-t , 
spring, balance weight-pan, aii'l ** 
its motion. 

The two shafts of the WHV K- * 
nccted to a prime movei 1 umt uti 
dynamometer raspootively, or Mi" 1*1 
may be fitted aa a dynaniomi'li't, ti* 
ft steadily running bral;o only i> i 
the transmission end. 

Tlio method of test in vn\ n 
aociimto than that of mea:tiniiF'-', f li 
and " output " torqneji, for in 



DYNAMOMETERS 



111 



arrangement, when tins efficiency of tho gear 
box is of llui order of i)7 pot 1 cent, no osucl 
results can bo obtained, because the errors 
in estimating tins two torques directly alVcet 
tlio calculated oflieienoy. 

Consideration of tho two cases will show 
tliat in tho latter, assuming tho accuracy of 
both tiwjiLo readings as 1 par cent, tho 
efficiency obtained will vary from 9J> to 
90 per uont if tho actual oflicienoy is 97 per 
cent. 

On the other hand, using tho more ami rate 
method, ami assuming lint accuracy of tho 
dynamo motor na 1 per cent, us before, and 
that of the torque measurement on tho gear- 
box frame as + 2 per cent, tho efficiency 
detonni nation will vary between 9(i-9 and 
97-1 per cent, i.e. a variation of only imo- 
twontioth of tho lirat method. In practice tho 
accuracy of tho lucnsuromcnt of tho torque 



of Hie springs, proportional to the tnnpio 
transmitted, being indicated by (Ins relative 
displacement of a pointer ovur a drum 
which carries ft slip of puper. Tho position 
of tho pointer at any time during an experi- 
ment in recorded by gauging a sin'ios of high- 
tension electric sparks through the paper HO 
that the magnitude of tho torque may bo 
directly calculated from tho known calibration 
of tho springs. A pencil or pen could not bo 
imoil for the indicator because of the difficulty 
of balancing Urn centrifugal forces called into 
play by the high speed of rotalion and also 
the fruition of the pun or pencil oti tho drum. 
Alternate torque springs are wound in opposite 
directions HO tliat the forties produced by the 
tendency to unwind duo to centrifugal action 
counterbalance each other ; with this orrniigo- 
mcnt ib was found Hint tho static and dynamic 
torquo calibratioiif! ngiecd with each other. 




on the rectangular frame can bo determined 
to about II per cent, 

Tho apparatus has boon usod to dotormino 
oflieioncies under different conditions of lubri- 
cation, and differences duo to lomporatni'0 
mid quality of lubricant have been ob- 
eorvcd, 

g (7) AERIAL PltOl'lil.LUIl BYNAMOJri'lTBIlS. 

In order to accnratoly dotormino tho perform- 
ance- and efficiency of airscrews, two dyimmo- 
motoi'H have been designed and made in tho 
Aoronuutics Dopartment of the National 
Physical Laboratory. 

Tho problem of the design of such an instru- 
ment involves tho determination of tho air 
npcetl relative to tho propeller, tho torque and 
the thrust, observations of each being made at 
tho same instant of time. 

In tho two widely different forms described 
below experiments were made on scale model 
airscrews about one-sixth full size. 

S (8) WHIRLING ARM DYNAMOMETER, A sec- 
tional drawing of tho dynamometer is given 
in Fig. 20. Tho airscrew shaft is driven 
through flat coiled springs S, tho extensions 



10 



The airscrew sliuft is allowed a siiiiiU usial 
movement, and it is m mipjinrlod that thin 
movement taken place with pxtremoly littlo 
Motion. Tho end of tlio shaft bears aj-ainfit 
an oscillating lovor, being directly controlled by 
the thrust spring b, tho tension of which is 
ndjustod by moans of tho micromotor msrew 
/ and two adjiiHtablo stops,, both the latter 
being insulated oloul.rically from the frame of 
tho instrument. 

When the thrust of the nii'Herow balances 
tho jjull of tho spring tho lover floats between 
the stops, but whon the thrust in too great or 
too small contact is mado with ono or otluir 
of tho stops and an indication ia thus glvon 
by means of a galvanomotor. 

ORcillations in tho torque springs duo to 
small irregularities in tlio driving, torque aro 
damped by tlio oil dash-pot K. Tliis con- 
sists of a series of concentric discs, altoniato 
discs being attached to tho slcovo carrying the- 
innor onda of the springs and to tho drum to 
which tho onto]' ends uro fixed. Tho osoilhitioiiH 
aro damped by tho fluid friction Lolwcon tho 
discs. 



112 



DYNAMOMETERS 






]>YNAMOMP3TEKS 




114 DYNAMOM'KTIM, UlimSH ASSOCIATION EDDY CttRRISNT JMAK13 



The apparatus is mounted on a whirling 
anii about ',W ft. in radius, and tlio cen- 
trifugal force on tins air.-surow has no 
component in tho direction of tho thrust. 
Certain forces duo to centrifugal action arc 
automatically balanced hy suitably placed 
masses. 

The airscrew speed is measured by means 
of the voltage obtained from n .small electric 
generator driven liy tho propeller shaft, or 
alternatively hy measuring this time* elapsed 
for cnuh hundred revolutions of tho shaft. 
Tho speed of the apparatus relative to the air 
ia ohUined hy moans of a Dines tube. All 
electrical and air connections are taken tn tho 
contral shaft of tho whirling arm, from which 
they a.ro again taken to an observing table 
whore fclui speeds of tho arm and propeller 
shaft ui'o controlled. 

g (!)) Fix MO AKJUAL Wim'HF.ijKa DYNAMO- 

MUTLJlt I'Oll USK IS A WlNI) ClIANNKL. - A 
sketch of thin apparatus is given in Fiij. 21. 
It consists of a small electric motor A bolted 
to a cradle, tlio ends of which uro attached to 
two hardened steel points bearing in tho cups 
of tho " Y " pieces M. Theso " Y " pieces 
ju'o rigidly eonnoctod to tho lower ends of 
tho diagonally arranged wires 0, tho upper 
ends of which arc supported from the roof 
of tho tunnel by stirrups carrying hardened 
steel points bearing in the oups I>. With 
this method of support tho electric motor 
is capable, if there is no other constraint, of 
a swinging motion in tho direction of tho 
motor Hhaft find also of a rocking motion 
about the axis passing through tlio points B, H, 
this axis being parallel to, and slightly below 
tho axis of, tho shaft. A spindlo arm K, 
projecting from tho underside of tho cradle, is 
connected by a strut and a " " spring to 
tho top t n spindlo clamped to tho head 
of an aerodynamical balance tho vertical 
head of which projects up through tlio floor 
of tho wind channel. Tho spindlo arm 'K 
(mil tho top of tlio balance arm are enclosed 
in a guard which is streamline shape surround- 
ing tho strut and " 0" spring. A revolution 
counter driven by tho motor shaft and in 
electrical communication with a boll enables 
tho rotational speed of tho airscrew to bo 
measured. To avoid any unnecessary con- 
Btraint of tlio moving parts of the apparatus 
the electrical connections to tho motor are made 



through tho mercury cups G. The scale of 
the mode! airscrew used with tho apparatus 
needs to be stioh that the motor with iln 
contiguous parts is completely enclosed in a 
shell of the model aeroplane hody.K, and such 
IIH to ensure miflicient clearance between tho 
surrounding shell and the moving pails of tho 
measuring apparatus, Tho body is suitably 
supported by liars from tho sides of tho 
channel. 

When measuring torque, the rooking axifi 
l.Sli of the motor and airscrew, which in 
parallel to the airscrew shaft, ia fixed 
parallel to tho centre line of the channel 
hy rigidly attaching tho " Y " pieces to 
the bars L. Tho brackets at tho lower 
end of the arm 111 and at the top of tho 
balance spindle are adjusted HO that the 
strut which transmits tho load to tho top 
of I ho balance arm is at right angles to the 
airscrew shaft. A direct calibration of tho 
apparatus may be made by applying a 
known torque and weighing directly with tho 
balance. 

To measure thrust, tho " Y " pieces nro 
detached from the bars L HO that tho motor 
and airscrew have freedom to swing in a 
longitudinal direction about the points 1) at 
the upper ends of the wires, and the points 
Jl of tho motor cradle. Tho brackets on tho 
lower end of tho arm JO and tho top of 
tho channel spindlo are adjusted so that, tho 
strut If which transmits the thrust to the 
tup of the balance is parallel to tho airscrew 
axis, A strut N, which is held in position 
with n " " spring between the bracket 
and the cradle and one of the bars L, pre- 
vents tho motor rocking about tho axis JiJl, 
Tho calibration of tho thrust apparatus may 
be obtained by applying a known thrust along 
tho airscrew axis and measuring directly tho 
airscrew balance. 

The air velocity in tho channel is measured 
by a tilting manometer. ,T. n. n. 



DYHAMOMETEH, WHITISH ASSOCIATION, fteo 

11 Dynamometers," (fi) (i.J. 
BYNAMOMET.EE CAIIS. See " .Dynamometers," 

. <G). 

LaiK'ashiro and Yorkshire Railway OO.'H. 

See " Dynamometers," g (fi) (v.). 
DYMAMOMKTJOU, HYDRAULIC. See "Il'ydmu- 



E 



Age of, deduced from Cooling, See " Heat, 

Cmidiiol.ion of," (12} (iii.) (a), 
foundations, Kfl'cet of the Percentage of 

Water present on. See " .[Motion," & 

(34). 



Temperature Waves in. See " Heat, 
Conduction of," g (12) (i.) (a). 

KcCKNTHIO G.BAII I' OR Suj)U VALVMS. See- 

" Steam Engines, Reciprocating," (2) (iii,). 

.I3ni)Y OlJBHKHT JJlIAKK POH POWHII MllAfUJIlE. 

MENT. See " Dynamometers," g (2) (vi.). 



KP:DY HEsrsTANCE ELASTIC CONSTANTS 



KIUJV- Hj'isrsTANOH. S(!fi "Shi]) Resistance 
and Propulsion," (IS) and (M), 

Ei>v VistJosiTV, 8ee " Mechanical Viscosity, 
I'Yietion," S(10), 00. (12). 

lOFi'KJIHNOLIJH Or ItJTUtlNAL COMHUSTION 

ENGINES, Table of Idcul Values. See 
" Engines, Thermodynamics of Internal 
Combustion," (4(1). 

Ei'ifroujNoitss OP PETKOL ENGINES. SGO 
".I'oti-ol Engine, Tho Water-cooled," (2). 



Y of A .HUAT-KNOINU, Tho efficiency 
is measured by tho ratio (Q, - QaJ/Qn Qj anil 
Q 2 being llio amounts of heat taken in and 
rejected respectively. H 'i\ T 3 bo the 
corresponding temperatures on tho Absolute 
Thormodynamic Scale, wo liavo for a revers- 
ible engine 



i x 

Thus tho omoienoy of any reversible engine 
working between toinporaturcs T L and T. a is 
TI_- T. 
T," ' 

Moo " Thermodynamics," (20). 
.lC[''FE(!ii'!N(Jv OF RANKINK UYULIJ. 'Sou " Bteam 
Engine, Thenry of," g (li). 



ELASTIC CONSTANTH, Kia 

T.ION O.I' 1 , AND Till*; TKSTLNU Olf 
MATKIUALS Otf CONSTRUCTION 

(1) INTRODUCTION. The reasons for Llio 
testing of materials of ooiiHtrncLion are vnrioiiH 
and do()cncl upon tho point of vlo\v in which 
tho i mill irtir appi-miohos llio subject. 

Tho dcHigiuir, in order to proportion tho 
parts o his machine or structure and apply 
hia tlieorotteal calculations, requires to know 
tho physical constants of the materials with 
which he deals. Tho aim of tho aoiontifio 
experimenter in to supply this data in order 
that tho theoretical researches in applied 
mechanics may ho applied to tho problems 
with which tho engineer, is confronted in his 
practice. Absolute results concerning definite 
properties of materials form the basis of 
scientific testing, 

Tho material to bo used in the construction 
of any structure can usually be obtained from 
several sources of supply and of several grades 
and prices. Tho engineer wishes first to indi- 
cate to the manufacturer tho class of material 
bo needs, and for this purpose ho supplies 
him with a specification containing among 
other things particulars of tho properties 
re([uired. The design is based on certain 
values for the physical constants, and tlicao 
values are the real criterion of tho suitability 
of the material for the purpose for which it is 
intended. Tho determination of tho constants 
is usually a slow laborious business requiring 



considerable skill and Htsionlifii) ability. Ap- 
proximate tests hiivo bnen devised, wliidi 
aro only intended to give a comparative 
indication of the physical properties i>[ the 
material. The results expected from UIOHO 
tests are inserted in the specification ; in some 
cases they approximate closely to the scientific 
tests. 

It is, obviously, important for tho engineer 
to bo assured that tho material supplied 
fulfils the terms of the specification, and for 
this [mrpoKo ho selects sample, portions of the 
material and subjects them to the specified 
tests. Commercial tcntiixj is therefore carried 
out to determine whether materials conform 
to tho terms of specifications. 

There is a further section of the subject 
which has been given a great impetus in 
the last few years, vi/. invcstiijalnry testing, 
undertaken to determine causes of failure of 
material in actual practice and to improve 
processes of manufacture ami design of 
machines and structures. 

The science of engineering is advanced by 
a systematic study of failures probably quite 
as much as by any other brunch of research. 
In investigatory testing, methods are employed 
to oxaggenile certain properties in order to 
compare them hi various materials with cum 
and certainty. These same jimperlk's can 
probably be studied by a careful analysis of 
the absolute icnults obtained by scientific 
testing, but tho profess is diflicult and cannot 
he attended with success without considerable 
practical experience. 

I. TKMTING MAIJIIINKH 

(2) GMNUKAij MiJTirons. There are certain 

methods of test which arc applicable to all 
branches of test work. The complexity of 
tho machines employed for these tests depends 
upon tho number of purposes for which it is 
intended to use them. This complexity is 
contingent upon 

(1) Tho variety of materials it is required 

to test. 

(2) Tho kinds of straining action needed. 

(3) Tho form and si/.o of the specimens to be 

tested. 

(4) The magnitude of the forces to be 

oxortcd and measured. 

(5) Tho accuracy required in the results.- 

By limiting tho requirements, the testing 
apparatus can ho made of great simplicity. 
.For instance, in a transverse testing machine 
such as is used for checking tho quality of 
cast iron in a foundry, the test pieces can all 
bo of ono si/.o, tho straining action is always 
tho same (tho test piece being broken ns a 
beam), and there is not a great deal of variation 
of tho breaking load. A machine such as 
this is simple and effective. 



110 



ELASTIC CONSTANTS 



noroiiftB in tho rcciiiiixmionts addn 
Hfidiliniial apparatus l,<i tlm niiiiiliino. An 
Hwi'HKory fin> iino pmpii.HO will often inlwfom 
with Mm miinimr nf tlm maeliim! fin- another 
purfuwi', thiiH causing loss of timii in making 
tlio iiRcoHHiiry adjustments for tho oxperimont-s 
in bund, involving great oaro in the sotting 
nf Mm machine and making it more difficult 
to handle. It is therefore in tlio intoi-eat of 
tlm IIHP!' (,<i eoiijudor carefully the functions 
ivhiob tho machine will im called upon to 
not'lurm, and l,n limit them tn a minimum. 
.In thin way ituii-Riist-d clficieiiey is obtaitied 
willi niiniiniini <;iiHt. 

TEio HiriiplcHt method iti testing is by direct 
loading, mid tbo curlier: rt-s(sn ns (ION on strength 
of inuloriida M'dt'n t'un'ieii out by U'i.H method. 
Cnlilco (10:18) an. I .Miiachfliiliiix'ik (172!!) miulo 
many li'sfn cm a .small sealo liy thin DHMHIH, and 
wliero if. nan nf.ill ho applied if. in tlm simplest 
and best inothod nf l('Htlnj, f avfiilalilo. Owing 
to MID difliciilty of Iminlling houvy loada it. !H 
(inly Hiiilabl^ fur n^ii \vitli wc;.ik niutoi'iidn. 

U'Ju'n ivt the lH^innin# of tlio miintennth 
Hnntiuy ilio ilomaiid tsnino fni 1 Icats on a 
lar/^or Hiialc 1 , it- \vnn ncwi.iHiiry to ooiiHklor nthoi' 
inoann nf npplyin HH: fnrno than by direct 
I<iudinj4, and within a fow years Lho 
(irrun}fninout [oiind ici minium 
wuro omhii'.d, vi'/.. ; 



(ft) Load applied by- hydmnlic pi-oas -no 
woiHliing dovioo, but loud ealoiihitwl 
from tlio ])rcssui'o on tlio rain, 

(A) Load appluul by yoixring nfc ono ond 
wciiffliin.^ Invcr at fcho other ond. 

(c) .Load ib])plic;d by hydniuliti ]iress at 
nno (Jinl \vHi(iiii}{ lover (it fclio ollmr 
ond. 

Tn LH1II molhnd (ff) was oitijiloycd liy 
Hntntdii it (Jo, for a i!]min-(!iil>l<i IcstiHg 
nuniliLiHi. Tlio arningoimmt for nn-iving at 
tlio loud ivas not (iajmhln o[ giving very 
, groat aocumuiy. It was nmsnasiiry to inakn 
an iilliMvaiKin tn tlm load, \vhu<li was dcchiodcl 
fixini tin* indi nation of a jit'osaiiro ganye, for 
llvo fridtion u tlio iiacking cif Uio mm or tlio 
cup loulhor, and Uio amount of thifi friction 
WIIH oxtromoly vailnblo, 

Tin) \Vhitwoi-tb hydnuilio tctitiiiK inaohinn 1 
iinfl l!iu 000-ton toiititig machinn of tho Union 
Hi'id^o Ciompany fib Athens, Pa., U.K.A., hotli 
uo l-lio satno iirinaiplo. Tho fiOQO-ton Olson 2 
fi<>iiipn\ssii(ii intioliiiit) of tho Geological Survey 
mid tiho TSuroiiii of Btandiirds, and the {100-ton. 
Olmsn eimipniflaion tefitoi 1 of tho Monfisalncr 3 
fnHtittilx) nt Troy doth rcaonl tho load by 
Mil! prcHHdi'n in tlio hycJnMiIio press, but with 
tln'ffo itianhiiu'H tho piVH-Hiiro is trammittod in 
n ifia|ilint;fin \vbuHo urea in oinallor tbau that 

1 Sim rivfc, I'rtw. !)ixl. -\lffh, Kny. t 18i)8. 

1 Kliflitlfwiilff fti'filf't, l''(lll. 11)1)11, li\. 

3 t'fiie. Am. Mae, Tent. Mitt., JIIOU, [x. 



of tlm main rani. Tlic p 
phra^ni EH niciiniirpd by 
iHcllidd (('} has been applied t 
machines by eliminating the inu>]^ 
having an nt'ciiraLcly Iittud ram aiuj 
with Kinall uloaniiUK!. .B_y UHinjr n j] (jn 1 * .-!?? 1 
Icakiigt! hctwccn tlm mm nncl. yylindi-i" i - '* ' * l<1 '" 1 ' 1 
the, friction to a practically ncgliffil)h> ii ' " ' ' * **'- v ' 
Tlic evolution of the other tw< i !*"?' ' '*'- 
nincliinc arriiiiffoiin'iits, (/j) and (c) j"r'< >:rl11 ^ ''*' 
dij'oofc ioadin^ method \V:IH duo tn (,|K. j ji i-r * ' l|(h " 
tion of tlic hivcr. .By placing , L J ( v HI '' "' 
between the l(;at ]i(!r;o and tho [< >.-* ' 1 '"' 
amount of dead ivciglil; iwjiiired wj tM (<* I ii" 1 '""' 
liy the riitio of the lcvr nnnti. Tit in ai I'J 1 '" ">'''' 
incnt, although <|iii1e miitablo fen- KnuLlt I 'i"-' 1 "'" 1 
jioHSKSsing littlo ductility, WHS fuu lt ri * " f ' n 
opiiii to tho objection that, ni\ tli<> r 1 1 > l ' " ' '"'"' 
sti'otishcH, tho position of the IOVIM- nll-i. lfl " rt i"f'il 
caiinut he adjusted. 

In UH7 ('a)itaiu .IJniH'ti <J>nKti-LH!tc I tv i 1 " ''I' 1 
teatiit^' machine in whicfh tho dofm-m J ( < ' M f| f 
the oahhi was nciitraliMcd, mid llio 1" >mJ 
ajmlinil, by incaii^ of Bearing at UIKI <>nnJ , ^^l^^l' l 
tho load wail inciiHiircd by a Icvt-r tit 1 [10 < >l I n-l. 
Tho win of ^I'jirinif way tho nn-f ]n >< I (| f 
si raining used in Amcrion <m niai^l i j n* "i "f 
tho lever typo. Tliti aiuiin ti.iTaii.jj;* ' i m* " > ' . 
although common on small niiu:liiiirH f" ' ^ ( ' N 
count-ry worked liy hand, had not, h* n'*- v'J', 
been nsod mi jin\v<tr-d riven in no him -.'4 1 1 1 it iJ 
reran Uy. 

Another method of oiuintenusliiiff |.lj<* Jii- 
forniation of tlm test piniscs \VIIH applt* 11 '' ' ,V 
-Lagerjlielm, of tne School of i\jin(>n Jv f, ^|.i n-Ii- 
holm, who ooiuhicLed c)X|ioi'imc.'ii(H in 1 MJ'^ 
on a 7-tou machine in whifdi a hydrmil i*' i-ji in 
noiilmliHod tho givo of th tc-.st ]ii.M-ci fsml 
ii]).|)Iio(l tbts load, which was imjauiii-i 1 *! Jiy 
u-PightH anting 011 a kmio lovur. AlKitil. I !i 
Hiime time, thut prineiplu waH alno ei M j i !. >_v <-i E 
l).y linimalr 1 in the coiiHtrucition of it. tit^i^liimi 
usod at Woolwich .Dockyard by tlio ]M,tf J 'i'n- 
foHfjor .ISarlow for some of ]un oxjiorim-c^n t-tt ivn 
tho strength of materials. 'l'hi nu-thcicl i.l' 
ciHisti-iicjtion ia, boiviivdi-, nlwiiys JIHS-:>C'III,I <=[ 
with thonamo of David Kirkaldy, who in 1 HlfU 
CTOcted, in ].,ondon, InH well-known i M j L* -J M iti 
of JOO tons cjipaeity. The cioinbriNLt. ic n i of 
hydraulic ram and Icvnra JUIH fiinoo ln'i-jj hi 
eonimon use in machines of ninny tlc-.-ii j- UN, 
tho chief dilYorenecs hi UICHO dc^igUF) Jiciitj": In 
tho arrangement, of tho lover or lovnr:i junl 
their position rolativoly to tJiat of 4\ti> |,-.ii 
piece, 

Tliomnasct, in ahnut the yciu- iMViT. 
moasLiretl tho load on tlm lovor by iiifjiiiH 
of a diaphragm piston with an ex t-i < .<! i M . < 'I y 
limited motion, and balanced- tho tojid , ,',, 
tho piston by a moreiiry gauge. 



1 Unrldw, Ntre.nalfi nf Malerirtla, Lomltm, IHf* I . n 
* .]>bnfltoiir, Lea Mftmt.r, p. 52. 



ELASTIC CONSTANTS 



T'Imory a feu 1 yearn later dispensed with the 
lever and transmitted HID whole Inad to the 
diaphragm. 'Kmory ' eonstraelcd a machine 
i if -I50 tons capacity in whieh the pressure 
nn the diaphragm piston was measured hy 
transmitting it. tu a smaller one in wlndi tho 
mercury yau^o of Thomasnet was replaced hy 
a syHlcrn of levers and weights. 

The liral; essential requirement of a testing 
machine in accuracy the luad shown l>y the 
machine should he an accurate indication of 
tho real load to which tho tout pioee is sub- 
jected, In ordcsr to obtain complete accuracy 
it in necofmry that : 

(1) Sim [ilo moans should ho available for 
establishing the truth of the indications of 
MID machine it should lie capable of being 
easily calibrated. This calibration may 
al tor with use ; if of the lever type tho 
knifu edges may wear or ho displaced, 
and, on a threo-ineh fulcrum distance, 1 per 
cent error in tho readings would bo caused 
by a displacement of only 0-03 inches. 

(li) The scnsiti VOIICMH in work- 
ing should bo adequate, i.e.. small ....' 
djn'oi'iMicert in tlio load nlimiUl ho _ 

readily indicated. 

Another donmililo feature is simplicity 
not simplicity resulting from a mem re- 
duction of tho attachments for tlio various 
tests, but that obtained by ensuring that 
tho varied voijuiromonts are carried out 
without undue complieiiliniiH. This not 
only roduiTH the pails liable to 
alteration with UNO, but renders 
tho machine capable of rapid and 
easy manipulation during test, a 
feature which is especially important in il 
machine to ho used for commercial testing. 
Other requirements necessary in a machine 
or commercial (esting uro t 

(ti) The. tests should bo nceossihlu from tho 
front of thfi maehine, and Iho scale and eon- 
Lrol lovers within easy, readh of the operator. 

(It) The lest piece -should lie easily inserted 
in the machine, i.e.. the method of gripping 
nhould bo Himplo and convenient. For 
laboratory work it in advisable that tho 
machine Hhonld bo conveniently arranged to 
tnke an autographic apparatus for registering 
the refill] ts, and should be generally adaptable 
tu all sorts of conditions which may from time to 
time bo neeeHSiai.'y for varied experimental work. 

Tho liability of tho testing machine to 
subject tho specimen to momentary shocks 
should alfwi he considered. Tho inertia in tho 
lever and weights (in that type of machine) 
may increase the stress in tlio test piece beyond 
that indicated by the scale reading of the 
jockey weight, Tho construction of each 
machine should therefore ho understood by 

i Hfin TUWIID, htst. MccJi. Kna. Proa., 1888, MI. 200 
mill 'US. 



tlio o]j(!t';ttor, and in skilful band. 1 ? i-jTurri dues 
td (his L'aiiMe ean be fcduccd to a very snifill 
urn nimt. 

(li) .HoniKON'1'Al, AND VlJiTIlJAI. M AIJCI LN 1'IS, 

Testing maubiticH may lio arranged in cithei 1 
of two ways : 

(i.) In which tho loud is applied hori'/.ontnlly 
JinriKontfd testing iniKjliiiniH. 

(ii.) In which the load is applied vertically 
vcrticstil Ifistin^ macbines. 

For testing long specimens it is itaiml to 
emjiloy a machine of the liori/ontal tyjid iii 
which it is neceasary to .support the tc.'.tt picsca 
and the grips which hold it, otherwise foi'cca 



A. Fined Leverage and Variable 



Centre of Gravity of 
lioalwtj Weight 




D, Fixed Load and Variable Leverage 



Movable Jocliay Weight 




C, Movable Jockey Weight combined with n. 
Loftil nt n Fixed Leverage 



arc applied to- the test pieco wliieh arc; not 
moaaurcd by tlio Ifrnd-niciiaiiiini^ uppuriitiiH. 
Tho vertical testing machine, however, IH ninro 
cmiveniont tu handle and, except in tho eir- 
C!iiiiiBtan<:os mentioned above, in fclw arrange- 
ment generally adopted. 

(4) MODERN TKSTINO MACHIN KM. "Modorn 
testing niaohinc'S usually consist of four main 
parts : 

(i.) An arrangement foi 

(ii.) An nrljuatmeiit to 
of the deformation o f 
provide that there ii 
point of altnchmeiit i 
weighing apparafcua. 

(iii.) A method of measuin 

(iv.) Holclora for connoetii 
(i.) and (iii.). 



118 



ELASTIC CONSTANTS 



Thi) varimiH l.y]ii'.-i of on1.mg machine difTnr 
in tlio wny in which UICHO reiiuinsrm'iita an) 
(Nii'j'Jml mi),, The (ii'.st find KOCIIIK! parts aro 
iiHiuilly combined, IIIK! tins toad on the kst 
piece w applied in oiii* ond eiMier by (1) 11 
Btniiiiiiur cylinder actuated hy a pump and 
aomuimlal.or, sc r<i w oonipMiftrtnL'. or oil pump 
(hydni-iilin rotary or din-el driven) ; or (2) acsrow 
^caring driven hy liinid or. by power (Hindi jis 

(III I'll '(ill-id mold]'). SermV power tenting 



Sttfo Roils 



Weights 
(W) 




Scraiu Gtmrlnij for 
flufadiU or Lowering 
tlm Stilo Jtatla 



Fin. '2. 

jinic-hitKffl iiro divided JiiLo two K<iiiorl 
ilin riht-tiry winnv mul the rotating nut. 

Tim him I or foroo cxorhid cm tho f:-ost 
in moiiHureil ()i inoro coniinnnly in (front 
.MriLuin, by a lovoi 1 m- Hyatcm of levers wkli 
wcji^lihi Di 1 ii. inovitlilo coiititcrnoiso forming a 
M'nif filing iipiiiii'M.tus i 

(/j) liy linlruiiung it with fluid proasuro ncling 



('.) liy irioiimirtnK this pn-MHiim of Uic (ill or 

in Mm HlniiiiiiiH (iyliiuh 1 ! 1 ; 
(tl) liy (inlcniliiliiiH Hi" loud from Mio nnjflo 
i'ihuuls wliioh u v.'d^liL<Ml jioiululiiin in lff(:o(l. 
nim'hinoH using int-tlioilH (l>) and 



Ij 



v*'i' 



1 ' 



(<) have tho advantage that t,] ,o V 
elutajici 1 to make than the woigh n) r 
machine, are practically frcu from 
force's^ and the load i.t automatically 
to tho stress. They, however, renuEi 1 
careful attention and calibration, line! n. 
sidored by tho Board of Trade to },n 
nil-able for nso when making acceptnntro 

(r>) TYIMJS OF TESTING MAOUINHM. 
f l't>ali>ig Machine..?.- By far tho lurge&L i 
oE machines measure tho load by 
of a lover. The loading of tlio It 
effected either by (n) adding separate v 
to a Hcalo pan placed at a fixed IUVUMI 
fixed leverage and variable load) ; (6) 1m 
single jockey which (.ravels along tin* ' (t * 
{-i.e. fixed load and variable leverage.) ; O" 
combination of (a) and (b). 

These arrangements are indicated (liiij-? 1 ''" 
maticnlly in Fiy. 1. With either of the nit;t-(" 
the following points must bo homo in iti irn I 

(1) The lover during the tc-nt will ttlm 
its position, and in order to seeuro i;oi)Ml 
leverage the points of application of t-lio J* ' 
must lie in a straight line, i.e. tho cmi t.-ro 
gravity of the moving weight and un,V 
cilgos employed must all lie in a strfti|-?li 

or, if the moving weight is hung from ti> 
edge, the knifo edge must travel aloiitJ 
lino. 

(2) Any addition of weights dufinj* i 
must bo carried out without producing 
on tho specimen. In those maidiiiicH it* 
weights aro added to the scale jiivn it in 

to curry thiw out by a mechanical amiri J-T* ' f i 
ftiiuh as is shown in Fit/. 2. 

In some machines tho load in monfmi'i^l 
the height to which a pendulum boh in iviif 
This can bo considered us a uiodi(i<;iLl i* m 
(ho levor method. Fig, 8 shows Jio\v it' T,VJ*H 
employed in the tests described in th-n JVrif-i:u1i 
Engineering Standavda Association, J{t ] M. *rt 
No. fifi. 

it is desirable that, on tho Hfi-mo mmtltiiK', 
the percentage accuracy of reading Hi** lojul 
should liis tho sanio with small ns \\'il.li liii'jrn 
specimens, and it Es therefore imual t.o n I-I-JLII;.>;M 
modern testing machines HO that Llii) J-UIMIM 
le-ngth of Hcnlc is ctpiivalent to at ICNIMI- |.\vu 
values of the load. This is earned out, i^il h^r 
by varying Iho leverage or varying Lht* l ^^ 
of tho moving poise. 

The leverage ia varied by providirijjr 
native fulcra, This method is in trod IH: etc 
the Wicikstoed vertical machino (KCO J''V/.. 
nnd consists in providing a third kiiifo 
which oan bo put in or out of gonr. *\Vlu<.|| if,. 
i-s in ])laco, the knife-edge distance SB lu-r^it uml 
tho machino ia arranged for use with wcjiilc Hpi>>i- 
mom, otherwise tho full capacity of tho in n 1 1 i (1|l 
is available. Thus the same ootintoi'iJoiwc^ 
roprosent say flO or 100 tons for fcli<^ 
travel of tho counterpoise along tlio lo\-<>i 



\\'ti i*l 



l*y 
.*i I, 

< >f 



n to 
J <IA). 



ELASTIC CONSTANTS 



111) 



in which fulcrum j. 4 used. 'I'Jio 
method of operating thu third knife edge in 
Bhown iti /''/;/. 4. The three knife edges arc 
En tho Hume lino, hut tJic movable support Y 
for tho third knife otlgo X is raised so that 



Spindle supported 
\ OH fla// Bearings 



Flexible Steal Strip 

^Gi-lpa 




press (iia shown) or by screw 

fullowiny are modern e.vnuipk's cf nnuiitini'tt 

which iiH(s tliis jifinoiplo. 

(ii.) "Awry" 10-loti ISltictric.allij ./>i : in\>i 
Simjla-levfj- Testing Machine. Thin inncihiiio in 
f-hoivn in Fig. (}. A is (ho weighing lover mid 
B tlie jniijo weight of 8'fO Ibis., wbieli is moved 
by a control screw 0. The; screw IH driven 
by hnnd at I) fhrough gearing .1C mid I 1 ' 
and n honked joint t\ 
which is pinned on n 
lino with ilio fulcrum, 
'i'ho straining of (lie 
test |>icoo is produced 
tJn'oiigh worm mid 
spur gearing )>y men i in 



ttl by Straining 
Cijlitttter 



Wfra rope attached 
to autoinatla gear 
to prevent weight 
fettling bach upon 



when it EH pliuioil in position by tho worm 
gem. 1 there \<A a alight clearance ovnr the support 
X, as shown in #';';/. 4 (II). 

Tho weight of tho moving poiso is varied in 
machines supplied by Messrs. W & T. A very, 
.Ltd. The counterpoise is split, and for small 
loads a part of it is detached and used us a, 
separate poise. 

In onlor to obtain a high incchaninal advan- 
tage, without making tho short arm of tho 
lever very small, some machines iiso a niiiliiplo 
system of levers, each with comparatively small 
mechanical advantage. Tt is therefore con- 
venient to divide lover machines into two 
motions, (1) those lifting a single lover, (2) 
thoso in winch tho lovers arc compounded, 
find to subdivide thoso sections according aa 
to whether the test pieces are vertical or 
liormmfcnl and whether tho load is applied by 
a straining cylinder or screw gearing. 

(li) SlNQLli-LBVREl MACHINES, (l.) Verti- 

ciil. ffig, ft shows diagianinmtiflnlly tho 
simplest arrangement of a single-lover machine, 
this being tho principle- adopted by Mr. Wick- 
fitccd, 1 It is n voi'liciil machine with a single 
hori'/.ontal lover A on top, to which ono end of 
tho test piece B ia connected. A movable ]ioiso 
G weighs tho load, which is applied to the other 
end of the teat pioco by tho ram of a hydraulic 
1 Just. Meek. Bug. I'm., 1882, p. 38-1. 



of fin olecLrio niol.i 
H, ivhoso contnil in 
located at I on flui 

fracture of tat piece standard near ti> ihn 
liand wheel propelling 
tho poise weight. 

Tho indicator J, -which filunvH the 
equilibrium of the steelyard, in idno 
close at hand, HO that the operator Inm 
all tho controls within easy reach. The 
free end of tho lever ploys in n Hpiu-n 
in the supporting pillar K. S|>riii(-n am 
Iirovided to take the shock when tbo tent, picnt 
briiiilts. 

Tho grips for the test piece urn uhmrn /il 
Land 11 ; UIOHQ are provided with atta^liiiicnln 
for tent pieces with either screwed or eiiilnr^nl 
ends. Tho upper grip is altncticd to tho IHVIT, 
while the lower one, which slides, in gulden in 




(B) 



the standard O, is connected to tho 

screw P. The second knife edge Q rcntH nn 

the standard 0. 

(iii.) "Denisans" 30-lan, Testing Machine.- - 
In this nmchino, shown in Fiffs. 7 and 8 t tho lmnl 
ia applied by a straining cylinder, tlio preHFinni 
to which ia supplied by a patent hydraulic 
rotary oil-pump. Tliis pump hafi a viirinhli' 



120 



ELASTIC CONSTANTS 



delivery in either direction whilst lifting (!<m- 
tinnously liriven in ojic dinwUim. The drivo 
cuti either bo by diroflt coupling to tin elc.etrio 



photograph i filled with 
(see $ (())) giving a short 
of either ;! or fi inches, a 
of 

this full 
can be 
either 
tonn. 



( | in 

Unit tl 
1 Ion j n 
IcngLh of the* 
armngoel |,f> 
a load of cii: 



the macliino 

linen add or! 



motor, as shown 
in /''/</. 7, or by 
a licit from a 
countershaft. A 
similar pump i 
used for driving 
the standard ' 
joekoy weight ' 
in either direc- 
tion ; td(i spend 
a t which i t 
travels can bo 
varied by means 
of a lovoi 1 placed 
in a ccuwoniont 
)>ositioiiL. 
Tlio niaoliino 
with 




toll-lulu dovicca, for Indicating to tlio operator 
tho fnnoUoiis of tlio various parts, as well us 
nil tho fun-lures Avliioh aro intlisponaftblo for 



(iv.) Jlitcffiotfa 100-ton Mnf.hhia. A photo- 
graph of t-bo nmcihine of this typo which is 
hiHlfillcil at the N.l'.L. JHwhown ini'V'f/. 1). Tho 
Jojul is applied by a hydraulic nun and cylinder 
which nni plnocd in n pit helmv tho floor level. 
A pressure f I ton pur sq. in. ia supplied to tho 




Kid. 7. 

N.l'.L. to prevent Ibo jocluiy wei^hfc accicloii t-n ll.v 
running past the end of tho suule in mit-lici- 
(lireotiou. When a considerable mimlior of 




by a Jiydi-juilicj piunn mid aeoninulfttor 
driven by an olnnlrio niolor. !) 1 .ho ominlor- 
yoiao in driven hy hand or inooluiiitcftlJy by 
ffist and lonso pnKnyf otmi'atfd from it miilablo 
''" ' ' f ti]ig, The inadiino HCOII in the 



\^^^ 



testa have to bo carried out, it ia usual f c >i- tin; 
operator to measure tho extension, contra o ti>n 
of area, etc., and enter up his results, wliilo i]n> 
emnitorpoise is running hack for tlio nnxt, t^ttl. 
It dotraeta from Ilia attention if lie bio to J.u- 



ELAflT 10 CONSTANTS 



continually on (,ho a lor I to atop the counter- 
POIHO at Urn light time. Tho gear is alinwn 
in detail in j<'iy. JO, and operate.* on the belt- 
throw-over gear. Tho shaft A operates tho 
gearing fin- driving tlio weight along, jilaced 
(it tliu end of the beam, and JH worked from the 
small countershaft (not shown) through bevel 
wheels 11. The sinking gear of the counter- 
shaft in operated by n shaft 0, ivhicli lias a 
handle (nut shmm) on Us lower end. A spur 
goal 1 on shaft A operates a screw JJ through 
fearing. Thin screw is so arranged that it 
does not rotate; but traverses horizontally us 
tlio weight is run along the beam. The screw 
carries a projection 13 working in n braekot 
I'' attaoho-d in the striking (tear shafb 0. 
Acljustivbln Inga G and H aro Jittcd on to 
this projcotion and am arranged so that wlicn 
tho counterpoise ranches the extreme end of 
its travel, in eitlior dirention, ono or other (if 
tho lugs G and H will rotate tho striking 
gear abaft nn<1 throw the driving belt on to 
Mte loose ptilloy of the countershaft, The 
lugs oaii hn adjusted HO that, for any serios of 
tests, the count erpoise will be stopped nt liny 
]>rcid(i(.ormirn((t position nlotig the beam. A 
[ibotiigraph of tin; gear in jtivon in ,/'V</. lf)A, 



T\Imiic1i exliihitioji in 18.^1, f*iii(.'i) \vhon a i:un 
aiilerablie nniii'ljoj 1 i>f siuiibiL' miH'hmcM Imv 
heciii ?onatrut'-t(!(l. Tin' firrnngoniciit <!' tii 
maohinu i.s iliu film led tljjij-raiiiiiinl.i<:ully in 
F'KJ. 11, from ivhich it irill he KCCU Ihul, 







(I) only OUR lever in ri'ipiireiJ for a itOO In I 
Lisvcragt 1 , inn! (^) by an JujrcnioiiK jirrangi'mcnl, 
the ranij lever, and Mcijrhls aic, all at oin- <>nd 
nf the ninehinc. It in Ihim a Hitnile iinilli'i 




FIG. 0. 



(v.) (florkfint/tl). Tlia We.rde.r Testing 
j)/i.'ii'e. Tho Wcrder machine, oxton- 
sivnly adopfeil in Germany, is a hori/.ontal 
single-lovor testing machine, in which tho 
load is applied by hydraulic pressure, hut 
in measured by dead weights on a single 
lover. Tho type waa originally designed by 
Lndwig Woi'dcr hi 1852 and exhibited at the 



to adapt the machine to dike teat ]tu!<:<>ii m 
any length, 

Tho test piece T is held at ono um'l Jn Ilu> 
framework of the nincliino A, and fit tlifs nUici' 
pulled. l>y the short arm L, of tho ktvcr, In 
which it is connected by a crossliefwl nni! louj* 
bolts, shown ih tho diagram liy n csoinunHiMn 
rod EF. At tho end of the lonjf arm of llm 



122 



KLASTTO CONSTANTS 



lovoi' hfing.H a soaks pan \V. Tho contra! 
fulcrum of the lover (i rests on the owl of 
the rain 0, HO that, as tlio test, piece extends, 



A (Shaft ffrlue to CattiitBrpotse) 



Tho test piece TH nulled fnmi tho urn in 
orosslioad V by four mils (two Hlmwn in 
plan aa T, and T a ) , these rods are connected 




Fia, 10. 



tho ram moves nut, carrying tho ivholo inoasur- 
ng apparatus with it. Tho arm L JH kept 
horizontal by tlio lirip of a level \vhioh is 




J'KI. KJ.V. 

fixed to id. ./'/'f/, 12 flhmvB a aootional elevation 
ilhiatrating tlio prinoipal Icnifo edges, and 
Fiif. l.'J gives a plan of the machine. 



vertically in pairs liy tsrosHlimulH Ui and U PJ) 
and pull through knifo cdgrs (', niul (! a 
on to a largo U-shapod liltiolc Q, to wliiisli 
the lever Q t ia I'igidly attuohcsd. .Hloisk (). 
liaa two ojieninga in it, through which tho 
crosshoada U, and U a pass. Thn horizontal 
lino through (3, and t)., MUBHOH through the 
axis of the teHt picoc. 

Tho whole aytitoiu of rods and enmahoiidH 
liangft from tho rain oi'dsahcnd at N t and J*J a 
on the traverse bar Of). Tho Nook (J 
hangs from thin bar by tho hnifo-edgo links 
I',, I'a (tho knifo edges being in l-lio anine line ns 
( V ^a)> its balance heing adjuated by llio 
sliding weight S. 

In the middle of Urn block Q the knife 
edge b is fitted; Una bnni-H against n uli'cl 
face a forming part o[ tlio ram croHslicud. 
This knifo edge is 3 nun. lower than tlio line 
of tho others. Thus (.lie ram eonn'ng out 
applies a load to tho teat piece through fho 
block Q, knifo edges C t and 0,, eivisHlieads 
Uj ami U s , and the rods T t and" T,,. AH the 
knife edge is 3 mm. out of lino wiih'o, and (! 
iv bell-crank [over is formed, the Htmil! arm 
of which is 3 mm. and tho long arm IfiOO mm., 
i.e. tho distance tho ncalo pan is away from 
tho knifo edge. 

It ia clear that tho length of the short arm 
of the lover (3 mm.) cannot be tliroetly ehcdced 
with sufficient accuracy, a controlling arrange- 
mont is thoroforo provided consisting of a knoo 
lover / a having a fulcrum on tho framo K 
and a ratio of 10 to 1. The knifo edges on 



ELASTIC CONSTANTS 



thi.H Ifsvtsr can lio accurately measured by 
ordinary means, and, to test tho accuracy 
of tho fiOO to 1 ratio, a tliroot calibration (tun 
bo made. 

Tlio I'ain C is 11-8 inches in diameter, (lie 
luilfc edgo h is l-|i. inches lung, and fcho 
two knifo edges 0, nnd O. a arc together 15 
inohus Jong, HO that the procure upon tlicm 
is about 7 tons per linear inch at full load 
(100 UIIIB). 

The pressure in obtained from two pumps 
worked !>y lia.iul or power and placed at the 
Kirk! of iho machine ti small one- of 0-4 
inch diameter, used for the full load, and a 
lui'gci 1 one, 1-2 inches diameter, for use up 
to a load of 20 tons. 

The arrangement shown ia for tension 
tents ; for compression tests the pull in trans- 
mitted through links from V to a back plate, 
or for short specimens Uio space between V 
and tho back of tho cylinder is utilised. 

(7) COMPOUND- LEVER JIAUIIINES. (i.) 
Vertical Mac/tines with /Screw Power. This is 



columns G, and G s attached to Hit! mill 
table. 

(ii.) Olnfin's gUOtOOO-lb. Tenting Mttctiiin: 
Fig. ]T> shows tlio 200,000-1!). Ol(!ii fo 
screw compound-lever tenting machine; of 
rotating nut type. 

tiirai)iin<iiMccJi(im'sm.~D,~\"> arc tho Hlrtii 
sei-owFi wliiuli firo attached to tlio pulling In-ud 
("J, to whieli imo end of tho spedinnn in 
attached.' They pass thrmigh holes at tint 
cornet' of tho platform E and thnnijdi 
openings in the lovers If 1 and hcd-plato <!, 
and enter the driving nufcfl II and II j, Hitiiiitrd 
below the latter. 

Tlio driving nuts 11 and II,, which im 
made extremely long to ensure u long life, 
are driven by means of gearing .IKMN 
operated by pulleys ami belting. An ciinli 
screw ia fitted with feathers, in longitudinal 
slots cut through tho threads, to proven t l-lusrn 
from turning, rotation of tho nuts OIUIJM'H thiv 
screws to either rise or full, carrying tlm 
pulling head C with them, Tho thrust nf 




Era. 11. 



tho arrangement of machine- which IB largely 
UHOtl in Ainorieji and is shown diagram inatieally 
in ffitf. 14, The straining mechanism is of 
two tyjics the rotating screw nnd the 
rotating mit. 

With the rotating screw machines, tho 
pulling sorowB jmss through uiil-s which are 
fastened to tho pulling head A. Tlio sm-ews 
aro keyed to and rotate, with the main gears 
through liearinyH in the cover plate, tluis 
moving tho head up m 1 down. 

In tho rotating nut type of machine, brawio 
nutH urn fastoniid in the main gtsai-s and rotate 
with them, pulling the screws, to which tho 
head is attached, up and down. Tho gears 
rest on long pedestals bolted to the base 
plate of tho machine, and in thoao pedestals 
keys arc (ixcd which prevent the sorowfl from 
turning. 

Tlio thrust, in each <;ase, ia talten on tlio 
undenionili sulo of tho cover pinto by ball or 
roller bearings. The rotating mit machine 
usually requires a pit or opening in the 
foundation for Iho uorows which project below 
tho base lino of tho -machine. 

Tho weighing apparatus consists of a weigh- 
ing table 0, levers .l)j and J) a , and a grftchmlcd 
beam 'W. Fni: tensile strain there ia also a 
weighing or top head F and two weighing 



the nuts against the tied - pinto G \ luldm 
by hall thrust washers. 

'{Hi.) Weigfii-ny A-pimrcit.ua. The woiySiiiii; 
mcohanisin is iis'scnUttlly tho sumo us that of it 
platform woiyhing machine. Tlio load on lln* 
test piece, applied by tho strnining inoc-lmiiinih, 
is oonimnnieatcd to tho platform JO oil her 
directly in ft compression test, or through tin 1 
medium of tho upper steel plato B (tn ivlui-h 
one end of tlio test piftc-c is wedged) inn I 
columns A in the tensile teat. 

Tho platform rests wholly on thrco nniiii 
lovers I* 1 GO cotistrueted us to tiet IIH H. innl" 
lever, and any prostmro on it is Inin-smiUi'il 
directly to them. Tlio knifo rjrtgca of only "ii" 
of these levers are shown in the ligum 

A second inulti[ilying lever V 2 In pluivd 
above and parallel to tho lover 1<\ mid in run- 
nected to it by a alimjp J a , Tin.) ruiuititm 
of the lover I^ is taken at K on a nhom; 
iron framoworlc which is secured tu tint HI-HI 
box of tho machine by a diagonal limn-. 
This framework also holds the support 1-j for 
tho fulcrum o the graduated steely nr<l F a , I" 
which the load is transmitted from lover I'' B 
by tho link n. 

A cylindrical weight AV, which nmii on n 
sercAVj' adjusts tho aero of the boam, whili- ti 
poise q t which travels on whecla, ImhuiccH llu* 



KLASTIO CONSTANTS 



K" 



UJ 



;;.i 

jr 




KLASTII! CONST A'NTfl 



load applied. Tho slcclyanl ix gradiifilod up to ( v i.) Thf. lin-min(//i(nn Ihiirrrniit/ I'M^HHt-U,. 
ll)(l,(l(ll) II is., itnd. nn additional \rag!i(, mi tho 'ftst'iity M ncli i >tr>..~ Tliiw in n iiiiiv^r.sal iinic'liinr 
.mil of Urn !(sv<-r adds a fiii'Mmr 1011,1)00 Ilig. | \ v ith a capacity of 700,01111 Ihs*. and lidji"; 
(iv.) !fi,rizttlnl <!oii/>j>/i<l l,c.r<>r Mw./ihte.x. \ ioriHion bnrs 2> ft. Ion;; and coliinniH :tll l'(, 
For Imlinj; !onj- pici-e.H, a horizontal testing i lung. Tlio spun for bi:mlin U-sl.s in ao fl., 
jiiiKihiim is rHKcnUal. In <mln- to 
oliviiito ili difli(!idf ii:w inti'odiKiod 
iiy I'lm .'iniall I\nffo-edH difitani.'c, 
nf Mm V\ 1 'i'i'(lt'i' inacliiiK!, mult. i|j|n 
lc\'('j' aiTiinH('iii("i)lH ni(( utaul. A 
lid! - (M'jitik )in r (>r is adopted to 
(sonvtu'l- (hi! lioi'iv.onlal Jortic into 
ji vortii'ril DILI-, anil Ihin is i^onihincd 
M'il'li Mm wi'iffliiiiif lever, cither ivitli 
in- will uint this introduc-liiin of 

Weighing 
rablo 

(o -M 

Oouei 1 ^' 



I IHI jirraiifijc-iiKiiil; dl two ina- 
uli iiHitti iff. liiit ty|K>iH given in /'Y//. 10. 

(v.) I, rt rift 1 , IIi'i::oiititI jWiicfiin&i, 

-In order to carry out lents /''nto^ 
on Iniilt-up Hti'iiotui'al im'inhiM's <if Screw 
(i praislinnl ni/.e, iiiaoliincn nf Itii'^o 
(!)i|)aisif'y lire R'i|iiinul, and fur tliis 
piirpoHii no inaidiino of IONH Minn 

:t()(l tons in of inndi use. 'Kxclndhif.; chain and iho wedge j.^ri|is diltu a niaxiiniini siwi of 
(vHl'hiH ninehiii(!H, the lirat example of la.i'e x Si" Hat. or :!|" (liiinielcr. 
Iniri7on(.i\l nnmliiucH hnilt in I. Inn country ar<i ; A ilia^raiiniiiitii: vimv nf tlio inai'liinn i" 
,''Hiim(!hiii(! of 'l(ll) tons l)iiilt in 18(11). given in /''/;/, 17 untl tnoru doLailwl (Iniwin^n nf 





Fio. 15. 



Tim 3f)0..tn inanlnno of llio Oiiiflcrvatoiro 
cira Arts ct Jttitieirs at PariH l)iiilt liy Mcsars. 
J. Buoktnn and Co. in 1004.* 

Tlio Avry ATftflhino a of 700,000 Ibs. in- 
(< tailed at lliniiin^hain Univoraity in 1SOO. 

1 Kiniiiii'i'riiHi, Srjil., 2, Itlll'l- 
! Kngiwer, May 2J, IHOO. 



llio sf.raininR and woigtiing mtjfsliiiiiifini in 
i'lVj. 18, 

'.I'lio ninoliiiin liaa a ram K at "no end mid 
tlio lever nystoin J) at thn other. Tlio heavy 
cost-iron lied XX linn milistantial 
HI-I fit citlwr ond wlmse tnpa aro c 
by horizontal columns YY with tlio 



ELASTIC CONSTANTS 



of about 40 feel, hetweon thorn without 
intcrnii'diftti) support. Them is thfii'eforo a 
oloar span id-mitf the top. and sideM, enabling 
heavy test pieces to IIR luworod in position 
by DID ImveUnr running overhead. To one 



L 




by means of four notched racks N 
tho fraino of the nmdiinu, which aro i 
head of tlio mm'iuid into which the 
No. 2 is keyed in any desired position. 

Oao end of tho tost piece ia iixoil 1 >J * ' 
erosHhead No, 2 and tht> oil" 
end to tho crrwahcad NI>- ** ^" 
compression ami tho 
No, 1 for tension. CrosshoafJw 
and No. ;t aro suspended from 
cdgos on the top of tho fraino A 
aro connected by teuaion nxlH 
which, whon em.sshead No. I! in in 



_. ._ , , , . o. n n 

Diagram of Greenwood and Batley's Horizontal tmnamlts tho Inad to tho lovor HX 



Testing Machine 




Diagram of Buekton's Horizontal Testing Machine 
I'm. id. 



tbo oylindcr L ia bolted, whilo 
tlio lovoi 1 syatom is Jlxctl to tho ollior. 

TJio loud in applied by hydraulic pressure!, 
At liiriiiiiiffhani tho town jji't'ssuru of 100 Ilia, 
pur W[uai'o inch in nvnilablu Toi 1 low load testa 
IUH! givos a to tnl thrust of 115 IOIIH. For tho 
full cupiicity of llio mneliimi an accumulator 
Blip ply if ton times (lin pressiiro is uaecl. Tho 
tliamotnr of thti rani ia ;}2 iiiohos and ita stroke 
(Ml inclioB* Tho main cylinder L, bolted to 
tlio Htiviuhirtl, forms part ill the inaohino frame, 



rl * 1 



thi'ough erosslifnd No. J IU K\ t,]n-> IMJIIH 
link .RB. Tho main link Ji.B ]>nll>+ "" 
tho top knife of a bell-crank li*v* >r 
through a hardened steel ])tm.HM! 
block (J. ThiiH, for coinprc!4Jc>ii> I Ji" 
load ia communicated to tho wm^li ' n l' 
appamtus from the ram by wu-v of { 1 ) 

sliding nicks N, N, (2) trnv'ollin^ *>* H ' 

liead Nu. 2, (3) tho test jjiodo, <*t > *!'*' 
floating orosshcad No. 3, and i-i>< IM I *r I '. 
(fi) orosshofid No. 1,- nncl f(n 
link U. 

The weighing anparatiiH eon wi Ht- 
holl-oriink lovei- A whoso i>nncipal knifo 
K!, C feet long, thrimts against n ])lal.n I 
in tho bed of tho machine. Tho loadiH i 
by tho main link Jl on to a knifo (itlf^ti J^a 
similar to tho principal knifo oclgo hut n. H!I> n't- 
distaneo abovo it and. forming with iti 1-1 m 
sliort arm of the Inver, Tho intorint^ I itL t. c 
lever and tho main steelyard D 11.1-0 ill. 
right angles to tho axis of tho machine*. r l'Jm* 
former lias its fulcrum on a milmtn n i nil 
casting 111 Uxed to tho lied of tho 



Hoto:~ Tl\a littermailiata Lever {Gl anil tint Main 

flauuttirnatta Steetejartl (O) aro at right angles to tho 

Counterpoise - axls of thg Maohlna 



< 


D' 

^j 


H 
C \ 





, S (No,1 OroasheadJ T <^ a 
&>. s <&* / 


3 Cross tiaa it 1 




A- 


-rV_-_-V"-"-"M ^-flffJ-i^-S-^ Tftyj _-J5 i Ti'.'. 


^Y 










H 


E 


G 


r 






N 




5 




"p-H j 


K^ 
Dell 




1 B 






J* 


-0 f/Vo.2 CrossAenrfJ 




H 


Js3Tn 


CrantiLvoeriM P^ J T *"' 
1 \\ N, 


\ 



K 
(Main ftettitf 



Aiixltittrfj 
it ft tr* 
M 



Cast Iron Bctl X 
PlQ. 17. 



Eind the main ram K, having an intomal 
dianuitor of 20 inches, moves over an auxiliary 
fixed ram IU whoso funotion is to jirovido for 
Mio rotnrn of tho main ram after tha test ia 
RompHt'iJ. !rho main I'ain is driven forwai'd 
by (iilitiitting loir-prcHsuro wator lichintl the 
Jixfiil mm. Tho load on tlio rn-in ia isom- 
innnioiitod to tho (.ravelling orosshonil No. 2 



and the load from tho boll-crank lovor JH 
mittcd to it by tho link nnd shaoklH < j , 
whilo tho latter 1ms its fulcrum nupporl 
by a column H on tho sido of the much iim*. 
Tho split counterpoise system (soo g ( 
has boon adopted in order to obtain mi tip 
Hoalo for small loads. In this cnse it in li vii 
into Hoven equal poises giving, serumLto l_y > 



E LAST 1C CO NST ANTS 



127 




jimxiimnn load <>i 100,000 Ibs., and when 
combined the full loud of 700,000 HIH. 

The counterpoise can lie moved by Imiul or 
operated moiilmnieiiHy through a screw, mid 
all, the movements are controlled by one 
operator at the lever end of the machine. 

(8) DiAi'HUAGM MACHINES. Diagrammatic 
sketches of .diaphragm machines arc given 
in Figs. l'i\ hi <!. Fig. lO.i represents the 
Thorn as Hut machine, 1 construe! ed about tho 
year -18,72, , in which tho load is communion ted 
through tho teat piceo. ( l<> a levor 1, tlio cuid 
<)f ivhicsh bearS on l.n" a , diaphmgm (I. 'I'lio 
pressure of the lever tin 'the _ diaphragm is 
lialanced ly fluid pressure/ the amount of 
whioh ia measured by a gauge. . 

Tho jU'jiillaml inaohinc (J'/ff. 19n> is similar 
to that designed by Thornassct except that 
the intermediate lever is dispensed with, tho 
pressure being (.alien directly on the diaphragm, 
winch ia consequently much larger. The 
ittnillard principle in adopted by Messrs 
W..H. Bnlloy & Co. in their 5000-11). SCor- 
Hydraiilio tester, and ia a very convenient 
arrangement for aniall testing pur|)osea. Tho 

1 Lei) a stem 1 , Les M&mix, p. 02. 



128 



ELASTIC CONSTANTS 



load i.-i applied to lh<* buck of tlm diaphragm, 
acid the prepare in Ilio diaphragm itbamhur 
i.'i miMLHiii'Cfl liy a pressure yungo or jwrcnry 

(1 column. 

1'i-essnri} flauf/e ... 

or Liiiiiid Goltiiitn Jl ".! '-"- 1 represents tho 



<>'' |l ' l 




Knirry nuicsliiiu:, the first ex- 
ample i>r which v>'un completed 
in ISV!! 1 ; i\< in n;nlly a coin- 
jinuncl hwr iimuhino with a 
liytlmiilif! Idvor introduced 

FldtlVCOIL till) tent pH'CG 1111(1 

(Ins a'c'iyliiujjc iij>jirii.tits. TJu* 

pull of Nio lHt )>!(!({) )! in com- 

Uiil l,n u tlinjiliragin I). "It is trans- 
fnnii Ihta hi n roihicor R, (,|io 



the Board was the acquisition of an 
tosting inachiiio whinii llioy nrdornd 
A. II. Enicry of New York. T 
ocunplotcd in 1870, nnd is niio 
largest mid most accurate tasting i 
in tho world. Unwin, fi-ftnc 
ing an .Kmery macliinc, Hti-i<l r '* 'I"" 
merit of tho Emery iimulinw Wl{> * 
that, while it had (icon HUM lei us 
much more dislk:at and Kcnsittv limn 
an oixlinnry machine as a ulininintn 
lialaniHs was in comparison wUJi " 
ymcor's sealoa, t.lim i-oHnit InuL ! 
the sanVc timo hcen obtjtincMl liy 
means w-Jiksli rendnred tho morn noimi- 
tivo niacliino loan linhlo to injury, 
losa liable tn wpar, and IOHH liable: In 
get out of order, than tho ordinary 



, 

on wliioh.iH hiiltuiaid hy |,]io lover systom. 
(i.) Kmarif Mack'num. '.riio iiivit Emory 



Tho principal 

Emery machine are: (a) An iifrii-ii 
nicnt of hydraulic chamhorH ninl tl 
plirayinH ahlo to recoivo lurgo prosHii 
and shocks without injury and 
transmit them to a convenient point 
measuring and recording. 

(b) Tho roplaconient of knife cdgi'tf w 
thin blades of sfccol. These were inU't*ilu 



f"i' 

il-h 
n!(l 



1 id. I On. 
Flat Plate "loiifoarlge.'i" 




Flat Plata Springs 



itmnhinn owc its 



, HtjarnttllcGlmmbera N Plata Sarlnas 
$ nix! Diaphragms ' J 



Via. JOo. UtiiRrnin of Ilmmy i\rnc1ilno. 



to tho llnilerl tStatcs 



to " ahi 

oliniiiiali! frio- 
tion and l.o 
-pint Plate prcsoi-vo hul- 
"t,nlfoai(<jos" finitely i] u , ful- 
crum ttlf'tU'VJtlil 

or diHtiin(?H jicc- 
eisoly an li I'tid 
ndjuHtcd, ILIH! 
FiatPlato to rcaisfc u rul 
" tinlfa edges" traimmit all tlm 
prcsauros iirut 
shocks to vrliidli, 
tho full! rn mil 
arc Hiihj ei. 1 ! toil 
witlioni in 1 (in 



BonnL for (o.idin^ sfnd, iron, iitul other 
inlH, who ontured upon their worlt in 
. Onri of tho most important notions of 



slightest degree impairing thoir sonHi 
or durability," 

Numerous machines have bopu maflo in 
tho United States since 187!) on tho K 



ELASTIC CONSTANTS 



129 



principle. Figs, 20 atul 21 show particulars 
o the more important working parts of a 
;t()0,0l)0-lb. vortical Emery testing machine ; 
detailed il rowings am given in Mr. Towno's l 
paper. 

(ii.) 300,000-lb. Kmcry Machine, (figs. 20 and 
21). fitrtiinitiij Gear. A tension fost piece A 
(A'/;/. 21) is shown between the shackles U and 
L of tin.' machine. Tho upper shackle U is 
attached directly to the ram P of tlio straining 
press, which is carried by two main adjusting 
guido screws M rising from the bed of the 




Elevation 



N 



VerHcal Section 




PIG. 20. 

machine V. The vortical adjustment is 
effected by means of tlio nuts N, which are 
geared together, and are rotated through a 
shaft and bovel gearing by a handle X. 

The- fluid pressure is conveyed to the ram 
by the pipes 1\ and T,, which have swivel 
joints to allow for adjustment of the straining 
cylinder, 

(iii.) Hydraulic Lever, The lower shackle L 
is secured to a yoke consisting of two blocks 
H and IJ connected by four steel bolts W. 
In this yoke the hydraulic support S is 
placed between the two beams Gj and G a . 
Thus the load is transmitted directly to the 
hydraulic support through tho yoke and 

1 Sec Towno, Inst. Alech. Eng. Proc., 1888, pp. 200 
and 448. 

VOL. I 



beams j the upper block 1L acting on beam 
(}, for compression and tho lower Monk Ji 
communicating the tensile load through 
beam G a . 

The yoke is scoured in its proper position 
by flat plate springs 1 which hold it slwuly 
laterally whiln leaving it free (o move verti- 
cally through the small range de-wired. Tho 
hydraulic support S (l''iif. 21) is sliuwn in detail 
in tfhf. 20 and eonsists of n piston .13 wlneh 
can move vertically 0-001 inch in a fixed 
ring and Imso block (N und K). A space 
of ()! inoh is allowed lielwcon tho piston 
D and tho ring N. 

Tho lower surface of tho piston mid the 
upper surface of the bnso block are turned with 
annular grooves and are lined with soft sheet 
brass 0-005 inch thick. Tho linings form a sac 
]jy being interlocked as shown in the diagram. 
The piston 1), while permitted to move vt'iU- 
oally, is seoiu-ocl against lateral motion by 
an annular diaphragm V at its upper surface, 
and the exposed portion of the working dia- 
phragm or upper portion of tlio brass sue nt 
its lower face, which acts as a flexiblo hingo or 
joint. Tho sac is filled with nlcohoi and 
glycerine nr refilled kerosene oil, and ihc loud 
when applied to it is transmitted to 11 smaller 
hydraulic diambtr or reducer ]( {/''((/. H)}, 
conlaJtiing a similnr thin 111 in of lunml, 
whore it is Ijahmeofl by the lover weighing 
apparatus. 

(iv.) Weiyliiny Ajijmnilaa.'nw :naximum 
load of tho matiliine is Ihim reduced to a maxi- 
mum of 10,000 Ibg. on thorcdueer, and this is all 
tho load that is conveyed to the fulcrum plato 
of tho main lover M (Wig. We) of tho weighing 
apparatus. Thin pieces of tempered steel ro 
tiacd instead of knife edges, and aro forced, 
under a pressure of about four times tlio 
working load, into the pieces Unit they con- 
nect. Tho relation of tho bcnnm, which havo 
a total multiplication of 20,000 to 1, is 
shown in the figure. Tho total reduction of 
load is 000,000 to 1 , so that very small weights 
aro all that aro necessary to keep the levers 
horizontal. 

(v.) Calibration. 'Kho hydraulic support isj 
tested with known loads, applied by a " rating 
niaehino," up to tho maximum capacity nf 
tho Emery machine. 'J'lio exact weight re- 
quired on tho weigh lover to bnliwco a, 
known load on tho miiehino is thus found 
by actual test, and the. poise weights nro 
carefully adjusted in accordance with thin 
cal ibratioa. 

Tho rating machine is a carefully construe toil 
dead-weight loading appliance. The weight 
was produced from standard weights accu- 
rately adjusted at tho IViinmu. of SlamlimlB, 
Washington. 

(0) MACHINES WITH NO WHKIIIINO ])M- 
VICR. Machines in tlua class are those in. 



130 



ELASTIC CONSTANTS 



which the kind is npplied by a fluid press, 
and t.lio stress in the specimen \ mkudated 
from the pressure (in the plunger. 

An objection to this method of tost haft been 



that errors 



results 



consists of throo main 




W 



T 10. 21. 



owing t tiio variability of the. friction caused 
l)y tlic nun packing. This objection lias now 
linoii overcome, in tho machine constructed by 
jrcHsra. Alfred .T. Ainslor & Co,, by using oil 
us Uio fluid together with an accurately fitted 
rain iind cylinder witli small clearance, thua 
eliminating tlio packing friction. 

(i.) Amslcr Tslhiff Machine. A fiO-ton uni- 
versal machine of this make is shown in Wig. 22, 



Knoll installation 
parts : 

(1) The press or actual testing machine P. 

(2) Tho oil pump forproducing the pressured,. 

(3) Tho pendulum dynamometer D for menu- 

Tiring the load from the oil proc- 
ure in (he pressure cylinder. 

(ii.) Th& Press, Tho press is 
fixed, to tho top part of tho 
machine, and tho movable omdlo 
carrying UKJ uppor grips is freely 
Biispondcd from tho ram by two 
rods connected by a croHshoad 
which rests on the top of the- 
ram. Tho bottom of tho cylinder 
of tho press is held rigidly to tho 
base of I be macbino by four 
round columns, which arc miidc 
heavy enough (,o carry the super- 
structure and tho maximum loud 
without deformation. 

The base itsnlf doos not take 
any of the load applied to the 
teat bar T, it i.s required merely 
as a support for l.lio machine ami 
to raise- tho working parts to a 
convenient height above tho door 
level. It is made in the form of 
a hollow iron casting with an 
opening in tho front for the re- 
covery of tho fractured test 
pieces. 

Tho ram of tho prows i.i fitted 
in tho cylinder with such pre- 
cision that no collar or cup 
leather is rctjuired to ensure a 
sufiioiently oil - tight working, 
Tho small amount of play which 
the ram has in tho cylinder 
allows a slight percolation of oil 
to luko placo between them ; 
tin's makes tho movement of the 
ram in the oylindor very {'any, 
eliminating friction and allowing 
an exact measurement of the 
total load to boinnde. Tho ram 
can bo rotated by a handle, HO 
that by occasionally moving 
it tli rough a small angle the 
formation of ridges, etc., i 
avoided. 

(iii.) Oil Pump, Tho press 
is operated by oil pressure pro- 
duced by a high -press 11 ro pump 
(O, Fig, 22) driven by an electric motor from a 
countershaft (for small maehinoa a hand drive 
can bo employed), The arrangement of 
suction ami delivery of tho oil is Riich that 
if all the valves are kept closed the oil is auto- 
matically short-circuited back to the reservoir, 
which is carried on tho pump stand. There 
uro also returns for the oil to tho reservoir 
from the top of tho cylinder duo to leakage, 



ELASTIC CONSTANTS 



131 



mid for tho released oil from under tlici 
ni in, 

Wnlor pressure nmy bo used to work the* 
niaeliino by making nr- 
rangeinont.fi for transform- 
ing into oil pressure for 
working the press, 

(iv.) The Dynamometer 



D 




,*-0 



Aypamtua. The measurement of. tlio Joacl 

in inatlo by moans of a pendulum dyna- 

mometer "D. Tho 

oil fruiii tho high- 

prcasuro pnmn is 

admitted to tho 

straining oyliutlor 

through tho dyna- 

mometer, BO that 

the actual pressure 

in tho cylinder is 

shown by tlio 

pointer which is 

operated by tho 

dynamometer. 

Tho pendulum 
dynamometer is n 
modification of the 
dead-weight gauge, 
which ia used lor 
calibrating press- 
ure gauges, the 
pondnlnm arrange- 
ment being used 
io automatically 
balance the load 
on tho plunger, as 
shown in Fig, 23, 
Tlio oil pressure is 

applied to a plunger P, which is kept slowly re- 
volving during tho test by tlio pulley Py, from 
which it ia transmitted to a yoke Y connecting 
two vertical rods Gj, G 2 . The tops of these rods 



nro attached through a ball-bearing coupling ID 
a shurt block lever H, wliic!) is rigidly scisiircd 
to a shaft J mounted in ball-bearings in (bo 
manometer frame. Tlic dcpir>.Hsion nf tlie 
block H by tlio pressure causes- the heavy 
pendulum B f.n bo deflculed tmlil it nasinncs a 
position of cij_uilibriuni. The point of sus- 
pension Oof tho pendulum can lie nlleretl FOUR 
to iiiei-cnHc tho iscnsitivcneHs of the machine, 
tho connection to the recording gfti'gc hdg 
adjusted at the aamc tinir. 

Tlio arm and rod A attached to tlio pen- 
dulum operates a pointer on a dial and tho 
dynamometer ' 9 a ' NO provided with an mito- 
gra-pluc recording apparatus R. 

As a rule each testing machine ifi accom- 
panied by a pump and sej)arte dynamomctor, 
but it is possible for several machines to use 
a single pump, if worked in conjunction with 
an air accumulator, and a separata dynamo- 
meter for each machine. 

For machines of largo power, i.e. 300 toils and 
upwards, Anifilor's measure tho load by the 
extension of tJio columns which cany tho top 
shackle. As these columns ox lendunder the load, 
they arc made to operate a piston in a cylinder. 
Tho shapes of the; piston and cylinder arc so do- 
signcd that a small relative motion between tho 
two causes a largo displacement of tho oil 
whitih fills the clearance separating them. Tho 
displacement of this oil is mado to work nn 
mdicalonvhicliiscalihratcdiii terms of the load. 




(a) 




FIG. 23. 

(10) TORSION TESTING MACHINES. Many 
universal testing machines of tlie lover type 
are fitted with a special shackle for applying 
torsion al stress, as illustrated diagram nmtically 



ELASTIC CONSTANTS 



in Fit}. LM, in \vhieh Win ttmjuc in applied by 
a worm mid worm wheel A and measured by 




Handle for 
Applying Torque 



Jooliey Welyiit 
(B) 



running tlio joukuy weight H along tho lever 
tii'in U 1 1 is usually, however, more oon- 
iiHc, H KE'pumto inaow'nc, and Fig. 25 




L<ro, 25. 

shows 11 in null i no of 20 pounds-foot capacity, 
mndo liy j\rHsrs. -T. Jliiokton Si Co., em- 
bodying Uio method ol test mentioned above. 

A mint lilllo 
in a h i n (i, (I o- 
Nignuil by Pi 1 "- 
feaaou Tliiu'Btim 
(tnd niatlo by 
MflBBi-B. W, H. 
Bniloy & Co,, is 
illusttratod in 
JV(F. 20. Thotoat 
ia placed 
two in- 
jaws, 

ono of wliich in 
rolii tod by band 
tliriiiigli a worm 
iinil win-in M'liool. 
Tlio twisl. I'H conniHiHtcntfid throiigli the test 
pieco to Uio othor jiiw on ivliich a weighted 
pniuluhini is) altaolicd. The rcaiatanco to 
/infli.n*in o tho pendulum oausc-3 a torque 



to be applied to tho test piece, niul tlui 
angle of tlio deflection of tho poiiclnlinii i;t 
ji ineasiiro of that torque. Tlio hifit*'y "' 
the tost is recorded niitoj/ra])hically (IJl " 
cliiirt attadied to a drain ivhieli in f-'^minxl 
to tho jaw wliich is movud by the ^etii" M'h(n. 
T.ho tblledtion of tho ]ieiuhi!iun moves n. ji^tmil, 
which JH secured to it, over a gnitJo (siii'vo 
fixed to the frame of tho nmcliinc in nucsh n 
ivay that the movement perpendicular tn tlio 
piano of rotation (that is, Uio heiyli t <} f ^' ll) 
curve) is a meiisuro of tho torque, -vvbilci tlin 
length of tho curve is ])roportional to the ini^lo 
of twist of the teat piece. 

The two machines described aliovo im* 
typitsal of all of tho methods em]>Io3 r i'tl for 
torriionnl testing nifusliinea. 

(11) 'L'llAWHVKllSK TES'lTNO MAOIU NUM.--- 
Although a transverse tenting nhaoldc? 4il r fiyw 
forms part of a universal testing eofc, annul; 
testing machine manufacturers supply hpi-c-inl 
inaohinos particularly suitable for tcatitif* (Mini, 
iron by cross-breaking. These muclmi-cM nnnliln 
cast-iron foundry liars to bo tested ru|'idly, 
and give reliable information mt i" 'In 1 
inochanicnl proportics of diu'erent inixtniTH. 

Such a machine, supplied by MofiJii'H. \\', 1 1. 
Bailey & (,'0., Ltd., is shown in l''i(f- 7. It 
is suitable for test bars up to 2 in. dcio]i, 1 in. 
thick, and 30 in. between centres,' and li'in 
a maximum capacity of '-I/SOO Ibs. An iipwiinl 
f{)rco is applied to the centre of tlio Iniiuii liy 
means of a screw, turned by a hand-wlitiol, lift- 
ing a central shackle. The reaction in ttiki'ii "H 
tho beam by two 
end supports and 
also on tho lover 
near lo the ful- 
crum. Tho load 
is balanced and 
.measured by run- 
ning the counter- 
poise along the 



piece 





lover while tho deflection is obtained from llw 
movement of tho screw which applies tho iimcl. 

(12) GBIPS son HOLDING TEST BATIS. AH 

much oaro should bo bestowed on tho tleHrgii t if 



ELASTIC CONSTANTS 



tin; H''i| IM f (11 ' holding Mm test liars UK on any (if 
tlio other nasfMilinl pails of tho testing machine, 
if n<!(iiimlts results arc, required, It is import- 
aul. that those should ho HO designed that tho 
resultant of all tho forces nets along the axis 
of the har, for, if this is not done, the amount 
of l ho ult.imato load is affected. 

'J'ho usual method of ensuring that this 
condition in fulfilled is by arranging for soino 
form of Nphorind or swivelling seating 





Fid. 27. 

th (i tost piece- and tho connection to the 
hinting machine. The principal objection to 
MHM(J of these soatingH is that they hnvn no 
protection from dust, scale, or other small 
pic.eos which are apt to bis scatlerod by tho 
limit pioeo on fracture. 

Jti tho 100-ton JSuekton inaohine (see (fi)) 
largo homisphorioal pieces, HI and H a , arc 
arranged in tho top and bottom holders, and 
to those pieces tho special attachments arc 
liLtod for test pieces of various hinds. 

(i.) Venn Ion SiuicklesPin Grips, Fig. 28 
shows tho oldest method of holding tho ends 
of pla-fco specimens. A hole is drilled at each 
(Mul of tho test piece for a steel pin A, and tho 
micLdlo part of the plate is reduced in section. 
Tho relation of tho size of tho pmholes and 
tho si 20 of. tho 
heads of tho teat 
piece to tho ro- 
duced seolion is 
such that the 
specimen ahvnys 
l)rcaka in tho re- 
duced section. 
This form of holder 
IB one of tho best 
for small speci- 
mens, provided 
cave is taken to 
oiiauro that tho 
piuholos are accurately on tho axis of tho 
induced part of tho test piece, otherwise tho 
Btroas acrnas tho section is not unifoi-m and 
tho s])cciinon tears from the edge whore tho 
stress is greatest. 

(ii.) WeAga <7n>. The ordinary method 
adopted for holding specimens of ductile 
materials is between two wedges with roughed 
surfmsi'S, as illustrated in Fig. 21), but it does not 
necessarily ensure that the line of pull is axial. 
In order to obtain tho best results, with this 



fii?! 



.Tost Piece 



I'm. 'IB. 



method tho following points must ho borne 
in miml : 

(1) Tho position of the wedges in tlm linul 
and of the test piece in tho wedges, 

i'Yj/. 20 (A) shows a sectional viow nf tho 
testing machine head witli the wecigo j;rip:i 
and test piece in position. Tho woilgo uripn iin- 
bearing their full length against tho head anil 




Fid. 2(1. 

tho specimen i bearing for the full length of 1 (in 
wedge grips, and this is the correct condition. 

Fig. 29 (B) shows the position of the wedgi 1 
grips when the specimen is too thin, and wliilo 
tho tesb piece bears the whole length nf Ihn 
wedge gi'ips, Hie wedge grips lire not heaving 
their full 'length against the head. .In I hi" 
crtso liners are used to koop the wedges ba<*l< iti 
their proper place, as in .Fig. 29 ((.!), lthoiij;h 
to obviate this difficulty most testing nuusliiiiMi 
are supplied with pairs of wedge grips fmi|j 
able for various 
ranges in tho 
thickness of the 
plato. 

If tho speci- 
men docs not 
hoar for the full 
length of tho 
wedge grips 
(Fig. 29, D) 
there is a tend- 
ency, on tho 
application of 
the load, for tho 
end of tlio 
specimen to bo 
crushed and a 
force to bo ap- 
plied to tho he ad 
which may split 
it. 

(2) The tend- 
ency f r the 
wedges to grip 

the teat piece more on one edge than (In 1 
other. 

This arises if the specimen is thickm 1 <m 
one side or through want of proper adjuHtmciil , 
when tho holders for tho wedges are- nplil au<l 
separate from tho head, as in the HmsULoii 




^SpHlOtoa 
-TestPJaoa 
Arrangement for Ifenilcrt Siicciiru 
[n IM Ton Bndhton Mnclllno 
/liao/ii!'l to Knife Edaf of inu< 




i:t<t 



ELASTIC CONSTANTS 



100-l(in inmiliino (/'Vr/. '!(>). To avoid Lhis 
difiinidl.y MfiNHi'H. Itiohlo .Kim, supply wedgna 
with Ji round fiico. [n Ply. 1)1 (A), G tiro the 
round-Mused wedge gripH uon turned in tlio 
HhiHskln 8. Another niclhnd for securing 
proper alignment, is u form of ball-socket liner 
shown in Fly, 8.1 (li). 




|>-(lf)3 fbi 
square or roiuiil 
specimens 



I'm. a I. 

.For round or Hanaro ductile pieces tho wedgo 
grips lire provided with serrated V-grooves, 
n shown in l<"ty. Ill (C). 

Tho end.s of the specimen tiro uswi-lly en- 
largnd, us shown in the sketch, but with mild 
Fiteol or iron this enlargement may be dispensed 
with. 

(iii,) Helf - aliffiiiny Grips. When testing 
brittle inatoriuls or for micui'iito experiment:) 
tho alignment of tho upedmon is cspcoinlly of 
importance. It in usual in those CHSCH to uao 
circular test pieces with the ends to fit special 

AllaaheiJ toSphartaa! 
Seat!i:ftln Tasting 
ttnohliie SlmcMif 




Fid. 32, 



Boated holders, Fig. 32 shows vari- 
ous iinitlioda. oi' innohiniiiig tho tost jiioco and 
altaeliiiig tti tho Htmoldcs. 

(iv.) A very 30-iim ttliatfdes. Tho arrange- 
ment of Avory's 10-ton shack lea is shown in 
A'/f/. 3;(. TJio luildoi 1 i\I if) nttnchcd to a link 
JinnyiiiK from IJto btia]n of tlici testing machine 
hy n jinnonil Jink. Tliis lioklor consiats of a 
fm'tfiritf nni<^liinoil to tnko n aplioriofd aoating A 
on wliioh tllo jmtl of tlio tewt picflo is talten 
through u tool nlccl stem .li and nnt G. 
"" ' -m is scrowod nl) N to take speci- 




men holders of various sixes. Two f<i' I1IH 
specimen holder are employed, vi/.. (') 
headed test pieces I) and (2) for sernivtul I 
pieces 1C. 

The shackle is also arranger! For UHO iv 
wedges. For this purpose tho nut, wtc 
seating, and holt 
L arc removed 
and wedges arc 
inserted, which 
bear along tho 
surfaces I'T! and 
1-IJ. A handle 
works in the boar- 
ing K, and is 
arranged with 
Ings which move 
both wedges up 
or down at tho 
same time. This 
facilitates grip- 
ping of the speci- 
mens and enables 

, 1 1IC.ULC1I 1 Cf- !!* > - 

tests to bo carried ,, 

out rapidly. 

The top holder, for connection to Ihn liwc-r, 
is shown in tho figure. The bottom lndili'1', 
attached to tho rani-straining rod, iv<n-l*>i nn 
exactly the same principle ; a slide in, limvt'vci 1 , 
provided for it HO as to keep it parallel lo Ihn 
vortical testing machine guides. Until IioMnvi 
are given in tho drawing of the testing nnu'liitii.' 
in Jt'ig. 6. 

(v.J X.P.L. Self-aligning 10-ton. 
The shackles given in Fig. It-t wero < 
tlio author for tensile testing, more 
for uso in experiments for the dotormimtli-mi 
of tho elastic limit and elastic moduluH. M*lit\v 
consist of a bolt A 
with a spherical 
nut B on one end 
and a holder for 
screwed or headed 
test pieces on the 
other. Tho nut 
boars on a spherical 
seating CI, which 
fits into tho shackle 
of tho testing 
machine, Tho 
spherical seating ia 
kept free from dirt 
hy being closed in at 
tho top by a plate 
E and at the bottom by a piece of wanli-lcnl hc>r 
F, which fits round tho bolt, Tlio \vittih- 
bather, although forming a dnst-pronf c 
allows free movement of tho nut inn I 
on tho spherical seating. Tho spates in 
bush is filled with vaseline. Those 
have been in constant use ami Imvo 
found to give every satisfaction, 

(vi.) Grips for Testing Ropa. Tlio 



I ) iy 




Pio. 



Imh 
)lit- 



ELASTIC CONSTANTS 



1S5 



of ropus or cables requires considerable euro in 
order (<i obtain reliable results ; it is important 
that the grips should not damage tho ends of 




I'lO, 35. 

the rope, otherwise fracture- will occur in tlio 
sockets. 

The tests are more conveniently carried out 
in horizontal machines, whore there in plenty 
oE available length, than in vortical machines. 
Serrated wedges (Fig, 80) nro used for 
gripping both wire and hemp ropes, and, to 
prevent thorn from being damaged, wooden 
straps of a suitable thickness and length 
are placed be- 
tween the grips 
and the rope. Jn 
order to seize the 
rope over a con- 
siderable length 
those special 
wedge grips are 
made very lung. 

Whore only 
vertical machines 
available a 



aeetect to Spherical Seatimj 
nu Atochina 




30 



are 

satisfactory way 
of holding wire 
rope for tensile tests is to use conical dies in 
tho shackles and seal the ends of the wire in 
them, as shown in Fig. 36, with a low melting- 
point alloy. Tho wire is first lightly bound 
with fine 'wire at about 5 in. from eneh end, 
tho end strands are then opened, bent over, 
and tinned. Tho rope is next set centrally in 



tho dies, with a littlo liro-duy, and a hard 
alloy of lead and antimony run in forming a 
solid ond. 

Ji'or hemp rope and small cables a method 
which is largely iisnd is to splice isn eye on to 
eacih end and tost 
liy placing a stoel 
pin ibrough the 
oyo. A more re- 
liable method is to 
roll the ends round 
specially prepared 
helically grooved 
drums and clamp 
them. Such tools 
nro supplied by 
Messrs. Thmis 
Olson Testing 
Alnchino Co. in the 
United States of 

America, or Alfred J. Ainslcr & Co. (Switzer- 
land) ; they tiro costly to build, but give 
accurate results in testing such innloriiils. 

(vii.) (Iripx for fostititj Chain in Tension. .For 
testing separate elmiu links or complete) chnins 
a piecB of steel bent into U form in passed 
through each of the end links. The open ends 
of the U-])iefit!H are then gripped in the (hit 
wedges used for towting flat ImrH (HCO i''iff. IS7), 

Wlioro it in notutHHary to oany out a eon- 
Bideraljle lunount of chain test ins, blocks lo 





Via. 38. 

suit the various sizes of chain are provided, 
which fit into tho heads of the testing nmdiino 
OH (Fig. 38). liy means of Iheao Mocks 
sections cif a chain can bo tcfitcd under a 



130 



ELASTIC CONSTANTS 



proof liiarl ; this in not possible with the 
U-lionk im.'lhnd. 

(viii.) GoiHprestiion NItac!,-fr,.t. Spherical 
shackles foi 1 compression te.its iii'o necessary for 




Testing Machine 
ioiuar tteuti 



accurate work. These either rest on tho lower 
shackle or hang from the upper shackle of tho 
testing machine. Care must be employed in 
using any of these arrangements t<i ensure that 
the axis of the test piece is in line with that 
of tho- bearing blocks and testing machine. 

ffiij. !)S) shows a 
ball - bearing block 
arranged to fit tho 
upper crosshcad of 
an universal testing 
machine; this tool 
allows for free motion 
in all directions. 

Test Tools. ffiga. 40* 
and 40n show two 
types of shackles for 
transverse testing. 
Fig, 40.4 indicates tho 
rnller bolster sup- 
pi irts and ./''//. 40n the arrangement adopted 
with Ihc JJiiokton vertical testing machine. 
In tho latter method it will bo noted that 
the pressure is applied in halves, at W L and 

Upper Head of \ 



stundat'ds A, A can bo iidjnulod t 

tiona on the beam .15 to give different loiigLhii 

of span L. 

As timber ia not homcjgcmeoiiH, four-point 
loading is usinilly adopted (ffitj. 41). This gives 
a large .span over which tho bonding moment 
is uniform and in which tho beam theoretically 




JI'KI. JOn. 

bends in tho arc of a circle, ffig. 42 is u 
photograph of these shackles /Sited to a 10-ton 
Bnoklon testing machine. 

Tho following pointH in regard to apparatus 
foi 1 transvorso testa slionkl be observed : 





W a , giving a mnnll central span .D of uni- 
form bonding moinoril. The object of this 
method is to reduce- local crushing of the 
teat piece T. In both arrangements the 



.Honking supports should bo iiNod ut the ends 
of specimens. 

Metal plates should bo provided, if mHmsary, 
to prevent a high intensity of pressure under 
tho point of loading or at the supports. 

IMIectoinetcrs or deformetors should n<it 
bo attached close to the points of application 
of the loads. 

If deflections arc to bo observed, it in ad- 
visable that the rate of loading nhould bo mich 
that tho readings can bo taken whilo the load 
ia being continuously applied. If a stoppage 
is unavoidable, tho time intervals should bo 
constant for tho teat. 

(x.) fihenr Shackles. There are two mothods. 
of applying n, shear stress In materials, one 
by a torsion test and tho other by direct 
shearing or punching. The torsion for- 
mula only holds for perfectly elastic bodies, 
and if it is used for tho breaking stress 



ELASTIC CONSTANTS 



ii figure greater than the real -shearing stress 
IH obtained. 

Various methods for direct shear arc in use, 
hut wltli these tlic shear is always accompanied 




by a certain amount of bonding and com- 
pression. 

(xi.) Teats of Bar and Plate. Fig. 43 
indicates a shear 
test tool for round 








specimens. Tho 



quiring slight mudilieation lo that shown in 

Pig. 43. 

(xn.) Text of very Thut J'lnte. An iirrano- 
nient for slicar tests on very thin phites or 
slices from a bur, used at the N.P.L., is 
shown in Fiff, <14. The lent piece T. is 
placed in a die JJ having a hm'denwi 
steel facing F. A hardened steel 
plunger P, with a long bearing in Iho 
die, is placed on the test piece. T'he 
hole in the facing (</,) m lightly tnpur 
(thti figure is exaggerated), and Uic 
end o tho plunger {./.,) is intulo ti 
good fit in tho hole. 

The gear is placed between ilio 
compression shackles of the testing 
madiiiio find the load measured, which 
enables the plunger to puali a liolo 
through the test pinco. 

If / = the thickness of Iho teat piece 
and W-the load; then tho shear 
stress = W/7rrf t (. 

(xiii.) Test of Timber in Slicar (see 
'section on timber tests, 027)). 

(xiv.) Torsion ShttrHes. Tl ic puaicst 
way of holding a torsion tost pieco in 
the testing machine is to Imvo en- 
larged ends, eilhcr Kijuare or round, with two 
key ways out in them (Fiff. 'tr>). 

(US) OAUHKATION or TKSTJNB 
The only satisfaetory nustliiid oE 
tho readings of a testing machine is by iming 
dead loads through the full rnnge, such as is 




<- J s- 






/' 


< 4'4 Parallel 


j 




t 




r 0-SOO 






^ frf/nw 

j.i"ia, 45. 


. 


/I 




1V B dlan 




sjicoinion A is clamped to a block B and, 
Avith the testing machine adjusted for compres- 
sion testing, the load is applied to the shearing 
tool C. The, test can 
bo arranged so that 
the spocimoiiia broken 
in either single or 
double shear. The 
diea T), a.a well as 
the shearing tool, are 
made of tempered 
tool steel ground to 
an edge. Provision 
is made for wear of 
the tools, and they 
tiro inserted in such a 
manner that they can bo easily removed when 
necessary for grinding, 

A similar method can bo used for flat plute, 
tlio form of tho shearing tools mid diea re- 




Alternative 
size of Encta 



adopted in tlio Emery machines, and this 
method from tho point of view of accuracy 
is above criticism. 

Several devices are used to attain the aa-ino 
ends. If dead loads arc not directly employed 
verification, depends on a proviona calibration 
of the (ievico used, so that it ultimately depends 
on a dead-load method. 

Noxfc to loading by dead weights tho em- 
ployment of calibrating or proving levers is 
tho most acceptable method. Tliia arrange- 
ment is shown in Fi<j. 40. '1'ho levers L x and 
L a , carefully constructed, rest on knife edges 
in a double chair C,, which itself rests on tho 
weighing table T t of tho machine. A singlo 
chair C a is placed on tho other knife edges 
and forms the fulcrum of tho lovers ; Iho nppor 
shackle C a of tho machine- is brought down 
on to this chair. A leverage of ten ia generally 
adopted for calibrating machines rip to (.011 



ELASTIC CONSTANTS 



torn eapudty, and a loverago of twenty up to 
fifty tons capacity, which is tins maximum to 
Hi is motliod of vci Ili cation \x usually 



Other methods of chocking are aa follows : 
(i.) iiy a standard tuxl bur made o alee! 
wlinsn modulus of clnstieity ia known hy 
previous experiment. A test nieco is liirnccl 
In lit tho li'sting nmduno, and of such a si/.o 
that whon Iho maximum load in applied to it 
llni limit i>f proportionality of h/ad to xl,en&ion 
will not be exceeded. An oxtonsonietcL* ia, 
iitti!il to tho tost piece, and readings of it taken 
at various loads shown by the testing machine 
Indicator. Those readings are (hen compared 
with those calcjiilfttcid from tlio iiioiUihm of 
olaslioity, mid a verification oE tho tost my 
niaoliino ttcalo obtained, This method is difli- 



Tli 



Upner S/iaciitBof Testing Machine 
(T-) 




In *H" *w 
W(-IVUIIH 



I 



h 



d w 
"t * ' ' 
]in*l 



uH to uiiiTy out cxcopt by persmiB skitlcd in 
Hiich work. 

(il.) With Cfushcra. Ttioso an; cylinders of 
oo(i]!r whoso dimimition in length with load 
is known. A sorics (if ci'iinluirrt mo loaded in 
tin) i!oinpi'iw.Hion nppamtuH of tlio inituliinR 
with varioii." viili'fi of tho load, wliioh nro 
not(!(l from the) miioliiiio iiulieator, Tfin nctiuil 
fnnios oxcrl-dd tiro dfiduiiod from Iho diitiiim- 
lion (if liHigth of tlio Ri'imliors, mid thcno aro 
oonijHircrt with tho iiHlications of tho uiftohine, 
(lii,) Jly a .Ven'ai of Tr.twih Test Pieces. 
Thiiso ttvo miidti in (liiplicnto aixl of varying 
diitnioforH, HO tluit tlio largest test picooaVill 
taint m-ai'ly tlio full onjmoity of tho innoliinc, 

'I'hoy nro all turned out of tho same Imr of 
IHMIIOHOHCOHS material, and one scries ia broken 
ill tho leutinir machine to lie isfilihra-tod, and 
tlin (lii])]i(!iito series teftt(l uiidcc tlio Hfiina 
coinlilidHH in a niachino whoso accueacy is 
knuwii. 

Hoth niotljoilw (ii.) and (iii.)nro sinij>lu, but 

(iru mil, in'iiiJiililo for ii greater acenraoy limn 

(il.iotit ;f'!i jiur (soiit. 

(Iv,) An improvement of (he, copper critaiter 

method liaa been suggested by Sehnlo and 



lii'imner, 1 who used wood in tho foriii *>^ ^' M ' Jtl 
of small thickness (2 to 4 cm,) as ^.I'liMl' 1 ' 11 *'' 
Wood has tlio unique property of ofl't^i 1 ' 11 ^ ' '"' 
samo rosistauco to crushing whujtlior i-.c^t-*" 1 ' ll " 
cubes or thin slabs. This method <i iMp 1 ' 11 -' 11 '" 
with all measurements of deformation \i'iii-'ti 
neceasittiro tho use of iiiBlrnmciUfj of ^r^^inii'ii, 
and by selecting wood well dried nncl w*t li"'il. 
flaws, an accuracy of 1 percent can IK <>!>' tl i jl1 '''- 
Messrs. Sohule and Brainier fountl i.1** 1 *- ' '"' 
wood of Conifcrao JK tbe most fliiifctxl>lti o^^'Jcn 
to iti regular structure. ]''ive or aijc -i >if**'<* H "' 
wood of each cross-sectional area m-(j 1*-rtlf<l 
in a standard machine as well n,et i 1 * ''''*' 
niiichino which is under calibrat.ioiu 
(v.) With a " Sta-ndanlising P.ox 
an instrument supplied by MCSHI-H, 
Amsler & Co. for q_uiok and 

ing of toatinu; 
It isessontiaily i 
test bar wJicmo 
iindor load i u & J l |-l 
measured by ita t lirnimi 
lion or iiim-oJiHt-. ii 
volume. It JH Ii I 
moreiiiy, aiul lui 
y.ontal ea])i]lnr 1 ' 
also jHirlly Jillt 
moron ry t 
on one 

inierometor, \vt i r It i tin, n 
plunger in and *>nU i>f 
the box, an tin* tlhi'i 
side. Whon the* iunl ci- 
menfc is st roH.no < I fi xiiill.v 
the position of * In* nn-i'- 
oury in tlip t^n f >i H i n v 
tube is altered owing ia the change in v* lu m"'. 
Tho position of tho mercury is then. rc'Hlinvil 
to the zero position by the micromotor. Tlin 
reading of the mieromcter is eulibmlft I u ntJci 
known loads, und this ealibratioii iinc^l in 
eonjiiiKition with tho standarilifinju; Ixix hi 
nhoek the trating macnine. 

Tho inethotk described above arc ii| ] >li*-u llr 
to most testing machmca, but with sinj^lci l<i v^r 
voi'ticiil machines a aimplo tost can In? c-uri ii>il 
out qniekly and acouratoly in tho f< ]] \i- in,^ 
Way : 

As tho load is weighed by a jockey -vvi'jjirlil . 
and as there is only one lover, it in only n CM < H>I u- v 
to verify the weight of the jockey and t-lio Mli.n't 
arm -length of tlio lever to onauro tin it lli- 
machino is reading correctly. 

(vi.) M'p.ight a/ the Movable Cou)itf.rjn>i.^f. 
This can be found by lifting it from tlit* l\' ( .r' 
with a suitable weighing maehfiio HIIH.J K-nc \\~\\ 
from a orano or, whore this is. incori x'^Mii^ril 
by moans of tho lovei 1 itself, in thci f< >l]r\s-j n{ 
way, Pirst balance tlio beam nncl ac'lj itMt ( hn 

' "A Now Jlntl iod itf comparinff tho lmll<> E L i IJ...-L 

of Tpstlntt Machines," I'roe. Int. Assac. of '" 
New York, I012. 



ELASTIC CONSTANTS 



vernier In Ker<>, then hang up a known weight 
from tho lioiini nt a measured distance from 
the fulcrum. This raises tho beam, and the 
cnunterpoiHo is run along until balance is 
dgiiin restored. 

]f \\' weight of counterpoise, 
i- hanging weight, 
f, = distance of hanging weight from 

fulcrum, 
Jj:= distance counterpoise is moved to 

restore balance, 
then W^r^x^/L. 

(vii.) Diftlnnce between the Kni/cJStlges. After 
llio hoam lias been balanced and the vernier 
fi<l justed to zero, a heavy weight IPV. is hung 
in Iho nhaoUlo of tho machine and tho counter- 
poise moved forward until balance is restored. 

If \V-woiglit of counterpoise, 

L = distance counterpoise is moved to 

restore balance, 
w t ~ weight Ining in shackloj 
/ a knife-edge distance, 
Ihon knife-edge distance - / a = TJ x W/w 2 . 

(viii.) Sensitivity. 'K\\a sensitivity of the 
machine unn 1)0 determined by finding tho 
greatest weight which can bo hung from tho 
tihaciklcH without causing Iho beam to move 
after it has been balanced. 

J. IT. Wielcalcod l found tliat with a 100- 
lon machine in equipoise, but unloaded, eo 
that the dead weight of lover and poise ia 
equivalent to tons on the knife edge, a pull 
on tho shackles applied through a silk thread 
lireiiking with a load of 3 or 4 Ibs. ia sufficient 
to raise tho levor arm through its whole arc. 

(ix.) Zero Error. Care should be taken to see 
tliut tho zero of tho machine is in adjustment 
before commencing ft test. 

II. ELONGATION AND CONTHACTION OF AREA 
(U) DUCTILITY, For workshop use a bend 
test gives much information as to tho ductility 
of a "'matorial, and requires very little special 
aj>]iaralus to carry ifc out. Tlia usual measures 
of ductility, however, are the ultimate per- 
cantngo elongation or contraction of area at 
fracture in tensile teat. 

(15) DISTRIBUTION or ELONGATION IN TJIE 
Tns-r UAH. If a test piece of ductile material 
in marked out in one-inch lengths and then 
tested in tension, it is found that it breaks 
with a neck or waist, and that tho increase in 
length of. tho section including the neck is con- 
sidembly more than at any other point along 
the bar. Observations for some bars are given 
in Table 1 , and results from them are plotted in 
Fig, 47, \\-licro tho stretched lengths arc plotted 
na ordinatca and the original distances along 
tho bar ns abscissae. Tho resulting curve is 
seen to consist of two parallel branches con- 
nected by a S curve, and it will be evident 
1 Prae, Insl. Mceh. Eng., 1888, p. 464. 



roni tho curve that the vertical <lislmii-n 
jetiveen the two parallel branches IB tli^ hint I 
^tension duo to tho necking of the Ic.st pincv, 
In Fig, 48 the same results are plotted in 
another way. The increases in length in eauh 




Distance of Batirje MarAt along Test Ha 
fljo/oro telt) in Indies 

FIG. -17 

inch aro plotted as ordinatoa at tlio conlm of 
each inch length and connected hy a ourvr. 
It is aeon that tho rate of elongalwm nt tint 
fracture is very largo, and that tho <mrvtJ in 
nearly symmetrical. 

From tho figures in Table 1 the pem)iili.'|(i< 
elongations on various gmigo longtlm can ini 




LeagtFi along Test Place In Inalies 
FIG. 48. 

calculated. Taldng tho fracture as ncvar to 
the centre as possible, these results aro nlvw 
in Table 2 and nro calculated as follow* : 
If tho original gauge length = L Jt 
t-ho final gauge length = L 2 , 

the Blongatioii = L.J - L,, 
and the per cent elongation, = 100(L a - I M )/ 1 -,. 



140 



ELASTIC CONSTANTS 



Tt will bo evident from tho table that tlio 
percentage* elongation is dependent upon tlic 
gauge length) decreasing as tho gauge length 
increases, and that fur strictly comparative 
results tho same gauge length should ho 
adopted fur liars of tho sumo diameter. Also, 
for strict tin mpn lability, the position of tho 
fracture should ho the same in each bar. If 
tho bur breaks near to the end of tho gauge 
length tho percentage- elongation is low. Tlio 
formula for calculating tho error involved has 
been expressed by Unwin l as follows ; 

" Let j bts the percentage of elongation in a 
gauge length L + 2JC, and e 2 the elongation in 
a. gauge length L-2X, the fracture being at 
tho centre- in both cases. Then the elongation 
in a gauga length L when tho fracture is at 
X from the centre in e = \(e. { -t-e 2 )," 

Tho results in Table 3, taken from Umvin'a 
paper, show tho magnitude of tho error. 
Unless tho gauge mark is in tho part affected. 
by the lonal contraction, tho effect on tho 
percentage elongation is small, 

g (Ki) HAUJIA'S LAW (ELONGATION OF 
GKOMKTHKIALLY SIMILAR TEST BARS). The, 
law connecting tho elongation of geometrically 
similar test pieces was first given by J. Barba a 
in 1880, who observed that similar teat bars 
deform similarly. It follows that, for cylindri- 
cal specimens, if the ratio of gauge length to 
diameter is constant, tho percentage elongation 
is alao constant. This is shown eloarly by tho 
results on a, mild steol and medium carbon steel 
given in Table 4. 

UnwJn sjiys a that " in pinto test bars, not 
strictly geometrically similar, the percentage) of 
elongation is practically constant, if the ratio 
of gauge length to square root of cross-section 
is 'constant. Tho form of cross-section within 
somewhat wide limits, if tho area is constant!, 
does not appear to influence tho elongation." 
(17) TlIK 10l.ON(!ATH>N K-QUATION. (].) 
Variation milk Gauge Length, The elongation 
of a test bar is made up of two parts : 

() Tho general extension, occurring before 

tho maximum load is reached, which is approxi- 

mately uniformly distributed along llio bar 

and therefore proportional to the gauge length. 

(/).) A local extension independent of tlio 

gauge- length occurring after tho maximum 

load has been reached. 

If L the gauge length, 

e = tho total extension, 

then e= + /)L, where a and ft are constants, 
the former for the local extension and tho 
latter for tho general extension. 
TJio percentage extension 



(1) 



1 "Tcnallo Teals of Mild Steel," Insl, Oil', liny. 
Proa.. MICM, t:)v, 176. 

' JinvlHi'B 1 .aw, Bra Univln, " Tensile Teats of IWlil 
btcel," Insl. Civ. Xg. J'roc., 1004, civ. 170. 



i.e.. tho percentage extension for a, given 
sectional area decreases as L is increased. 

(ii.) Variation with (Jrnas-ner.tion.- Only tin* 
local extension is affected by the cross-sectional 
dimonsions of the test piece, i.e. the term . 
in equation (1). 

Since tho local contraction is proportional 
to the linear dimensions of tlio cross-section, 
and tho extension is not affected by tho form 
of the cross-section, 

where A -the cross-sectional area, 

c = a constant; 
i.e. for dissimilar test bars 

% elongation = 100*- = 100 (~v- + >> 
This formula is true provided 
(ti) Tho gauge points arc not too close to tlio 

enlarged ends of tlio test piece. 
(b) The length L is not so short as to full 

within tho area affected by tho Iminl 

contraction. 

Equation (3) is in agreement with Burba's law 
for similar tost pieces that, when similarity in 
maintained, the percentage elongation in 
constant because, in that ease, A/A/1;, and, 
therefore, c becomes constant. 

Unwin a gives tho following method of leant 
squares for calculating tho values of l> and <:, 
in the elongation equation, from a Bories nf 
observations : 
This equation is 

e%=q + 6. 
.|j 

For simplicity, let VA/L^n, and suppose (1m 
elongations have been observed for M gaii^n 
lengths. Then tho most probable values of 
tho Constanta are given by the equations 



Applying those results to bar H-l (Table L 1 ), 
whoso diameter^ 1-000 in. and area ^ 0-7fifH 
sq. in., and percentage elongation on 
3* = 41-0 (J'^Sl-8. wo have 
4*= 3(1-5 7* = 30-1 L \'X=:0'H8()3 
B* = 3-t-0 8"- 28-8 J amlM = (l. 



L. 


1. 


e. 


fit. 


fl. 


3 


-2054 


41-0 


32-J10 


0872-1 


1 


2210 


311-5 


8-088 


O.I!) 10 


5 


1773 


31-0 


11-027 


o;iM;t 





1477 


SI -8 


Hilld 


02181 


7 


1200 


30-1 


Jl-810 


01003 


8 


1108 


28-8 


:HDI 


01227 


2 = 


1-0794 


202-2 


37-022 


2I70H 


1 "Tciisllo Tests of Mild Mtuel," last. Oir, Knu 
Prof., 1001, civ. 203. 



ELASTIC CONSTANTS 



141 



TAIH-K 1 

BXTKNMOJTS ON l-INOFI LKNOTIIS AT DlKKBBKH-J! 1>IBTANKS FIIOM Tllll Fl 



No. of Test 


Diameter 

Of T(!Mt 


Yield 


'Ultimate 


UxtfiiiFilon In Indies In oacli Indi 


I'toco. 


Iliulltiti, 


I'OI IB/til). 111. 


Tons/Mil. In. 


(l-l 


1-2 


2-3 


!M 


4-5 


fi-n 


(1-7 


7-fi 


04 


1-000 


22-9 


47-1 


08 


10 


20 


-23 


-12 


-10 


-12 


13 


71 


0-909 


14 -6 


22-9 


-15 


1/5 


22 


-48 


2 


20 


IS 


IS 


8-1 


1-000 


10-3 


20-0 


'-20 


24 


117 


SO 


27 


23 


21 




5)2 


1-000 


15-2 


24-7 


24 


-20 


30 


78 


SI 


20 





Totul 



1-08 
1 -84 
2-30 
2 -67 



(The fracture was included ])elwi:cn 3-4 in cnoh cnso.) 



TAIJI.B 2 

PJ?UOBSTAOB UXTENSIOK ow DUTPBRISST OAUOB LHKOTHS (nTor.uniNa FRAOTURB) ON 1-i-vcn 
DiAMETint BARM. HKE TABI.K 1 



No. of Tost 


OiuiKfl Loniith In Indies. 


3, 


4. 


fi. 


0. 


7. 


8. 

1H-B 
2H'0 
28'8 
33-4 


04 
71 
84 
02 


18-3 
32-7 
41-0 


1(1-2 
29-5 


15-0 

34-0 
40'0 


25-2 
31 8 
37-2 


130 

211-7 
301 



El-OKaAITOK PKIIOKSTAaK IN 8 IHOIIEH, WHEN TUB Fll.lCTUIiH 1H NOT \'t THI1 (!|)NWlli OK THE 

GAUOM 





instance- of Fracture from Centre of llnr In Indies. 


No, of liar. 


0. 


1. 


2. 


3. 


4. 




Fracture at 








Kractiiro at 














2301 
2362 
23(53 
231)4 
23C5 


29 -2 
20-5 
29-8 
26-3 
29-0 


20-1 
205 
20-7 
25-3 
29-0 


28'0 
29 -fi 
2Q"8 
25 '3 
20 '0 


23-1 
20-1 
29-2 
1M-4 
28'B 


23-9 
24-4 
20-2 
24-1 


2300 
,2391 


2(1-7 
30-5 


20-0 
30 '5 


20"7 


28 -3 


23 -fi 



TESTS ON Siim.AB TBH-C PIEOES 



















No. of Test 
PJcflc. 


nimnetor of 
Test Piece. 
]) Indies. 


Clause 
Length. 
L Indies. 


Entlo. 
L/U. 


Yield Stress, 
Tons/Sq, In. 


fitrcss. 
l'ons/Sf[. In. 


ils tens ion, 
]?cr cent. 


Avon at 
li'racture. 
l.'or cent, 


B10D 
B10E 
B10F 


550 
420 
-330 


4-0 

3'5 

2-72 


8-30 
8-33 
8>24 


28-41 
28-88 
29 '01 


51-G9 
51-27 
61-70 


17 4 
17-2 
1C-8 


38-4 

,17 .fi 
JO'S 




C50 


4-0 


8-30 


21-26 


26 -52 


ilS-2 


70-4 




420 


3-i) 


8-33 


20-fll 


20-27 


32-8 


08-7 


A9F 


330 


2'72 


8-24 


21-OG 


26-flO 




07-8 



142 



ELASTIC CONSTANTS 



, _ (li x H7 -!)2) - (202-2 x 1 0794} 
~ " 



_ (202^3 x -21 79) - (T7;<)2 x 1-070) _ 99 

((5x'2J7!))-]'iuT> """"" ' 

and tlioroforo l.hn elongation equation for Ibis 
Imr (if nuUoria.1 ia 



*^ /[) T 1 & I 

(IK) CONTRACTION OK An ISA AT l^i 
..... If it i.i l!u> initial nroa of the trat bar und 
A 1.1 10 jmiiL fit tho point of friifituro, then tho 
reduction iiroa in wjual to (a -A) niut tho 
pisruonUyd rod tuition of area 100 x{- A}/. 
If ilio material ia porfiMiLly phial ic tho per- 
(imtafjw <:ini traction nf a-rou is c<[iml to tho 
porc!*mtii|JO nlongation where tho latter is 
wilmilulud oil. the jiiutl length of tho tost bar, 
/.. inOxfrt-AJ/n^HWxfl^-.J^/La. (F^and 
L* nn> lliu initial und linal lengths respeulively.) 
Tim ]miof of Miis in an follows : 

This volume of tho test piooo is assumed to 
ho etinatmit, tltorofoi'o 



A 



A L, 
- ^ 



caoh from unity, wo havo 
L, 

" 



Tho ngreemont IioLivoun elongation nntl con- 
tratstton nf urea in only for tho short part of 
Ilia Hjinciimon whoi'o thorn is plustio dolorina- 
tion, ami it doRH not apply to groatnr longtlia, 
I'rofnsHrtr Klliot [ IIHH givon IL tuotliod of cal- 
iniliL(.in/,;tho (iniiHtuntJi A ami <; of tho o]ngoti<jii 
(!(|irati(in (fl~WA/L-f-&) H-lion (Jio (siongalion 
in only knoivn on nno ganpt Jongth togothor 
with tlio onntmotion of arm of tho teat bar. 
Tho moUiod (hijinmls upon fclio assumption 
of u vahio for tho original IcnKtli of tho 
Ofmtmotod ni^ion. TnldiiH Uiis as m\^A, 
lOlliot found tliat m varind from 0-0 to 2-0, 
iiml iulo|itiiig tho valuo of 1-97 ho obtained 
vnry fail. 1 ngrcomont with rcsulta provioualy 
jiiiljliuluid Ity CTnwin. 2 

TTL. L J U001!l)UItK IN (tlU)TNAHY COMMKllOIAL 



Ooitunoi'dial (Celine,' in iindortakon primarily 
to Jimwrtaii) if tlio nmtnnal is of tho quality 
r<;qnir(id liy n HpixfilicaUon, T'lieso inapoe- 



Fid Jli'laMnn nf llio ('on.itiuilH or t.lio I 

11 tt) {I'oiil.mtitJoii of A roil," Inst. Civ. Jitty. 

Illl. flvlli. 'Mil. 

-Hill! Touts of iMIIil Stcur," Tiint, do. fine. 
' civ. 175, 



U-.V 



lion or reception train have to IKS 
([iiinldy, and RIB principally dime tod l<> 
indieatioiis of tlio strength und ducjt'i 
tho iniitDilal. 

(19) I'LiEl'AHATION A~ND SjlLKCTlON Ol'' 'I' 1 '" 1 ' 1 ' 

I'njCES. Tho tnst pieces must bo sole;*-? *-*' . Ht) 
us to givo a rdinhlu indication of the m n-l' 1 " 1 '" 1 ' 
na awliolo. Rfiinpliiifr i^ inhci-cntly im jid 1 ^' 1 "*' 1 ' 
nntl is therefore apt to emiso" di(Ji ( * 11 ' t''' !J - 
Sainplcs should ahvuya bo taken and Bi*- nl I l( ''' 
in tlic ])i'i!ftcnce of an inspector ncthif-C "" 
holi alf of tho piircluiacr, and Iho ro ** I ' * * ' l '' ' 
ha safeguards to avoid heat troalriieu & nr 
other inaiiijnilation after selection. 

Tho minil)Di' of testa should bo sjicirri Cii'd, 
and, in order to cover orror.i whioli arc* Ji '<*'',>' 
to arise, limits should be allowed on l-li" t<'itt 
resulla, and ju-ovisioii made 01- ro-io^*' 'f 
necesaary. A usual clause is that, almtiltl t '' H ' 
test pieuo fail to conform to tho s|)(jo.iftc.!ii-i-' (tM J 
tlio contractor Hhall havo tho opportuni t-.y f 
two fin'thcf samples being selected 1>.V *'''** 
inspector and tested at tho mamifiH'l-'iH 11 ""'^ 
expense. Moth of these samples jmiHfc jut."^ in 
order for tlio consignment to be accept*!;* I- 

Test pieces, if to he taken from a Hit.ni pin, 
such as a tyro, axle, crank-shaft, oto., wZioiild 
bo cutout hy cold sawing or drilling, unit Hiili- 
secp,iently prepared by milling, turning* n|< 
planing. Should whcaring bo unavoidnJilf. tm-ftt 
must bo taken to ensuro that tho 
not bent, and that tho sheared, 
entirely removed before testing, 
oxyacetylono blou'pipe shonld nob bo 
as it alters tho structure of the inaLiu'Uil for 
from 2 to 3 in. from tho out. 

Iron or stool plates arc usually teuton! ^>>(']i 
in tho tlirootion of rolling and acrosM it-, iintl 
with cast iron special bars are mado fi'inti cimfi 
east for transversa test. For mint! imitorifibi 
s]iccial bars form part of the canting itntl arc 
aftci'wai'ds cut oft' for testing, but it EH iitmnE 
to specify the position of theao IIHI-M niul 
whether they are to be sand or chill (SHHtin^H, 

Por apeoial testa some form of beat t-roiit- 
ment, such ns nornialising, annealing, OT f.citit' 
poring, may bo required. 

Annealing moans reheating followed Jj.v "Iciiv 
cooling. Its puiposca may lie either to I'oifitivi^ 
internal stresses and induce softne.HH, c>? n <i> 
roflno tho crystnllino structure. In fclio luttcr 
caao tho temperature used must axoocd 
upper critical range, but not more thti.ii 
50 C. 

Normalising moans hoating a stool 
previously treat nd) to a tempcraturo 
its Tipper critical range ^but not mnro tlimi 
50 C.) and allowing it to cool freely m a.ir. 
is desirable that tho stee-l should soak (it 
renuirod tomperature for about 15 

Hardening means heating a steel 
normalising tomperatute and cooling 
less rapidly in a suitable medium, 



]>,v 



ly 



|l. 



to 



ELASTIC CONSTANTS 



143 



wiitcr, air, or oil. Tempering is lo reduce the 
hardness and increase Iho toughness, and is 
carried out by licating the stool (however 
previously hardened) to ft temperature not 
exceeding HH carbon change point. 

$ (20) TENSION Tr.sTt;. The data ordinarily 
observed in a tensile teat for reception pur- 
poses is 

Yield load. 
Maximum load. 
Elongation after fracture. 
Contraction of area, at fracturo. 

If (21) YII;I,D POINT AND ELASTIC LIJHT. 
Vury often there seoniB lo bo confusion us to 
exactly what is meant by the elastic limit and 
tht) yiold point. It is a common practice for 
the elastic limit to bo specified when what is 
tictiinlly required in the yield point. The actual 
elastic limit can only lie obtained by the use 
of delicate strain -measuring instruments (HCO 
(62)) ; the yield point is slightly higher than 
tbo cltislie limit, and is the point at which 
there is an increase in the extension without a 
corresponding increase in the stress. Tliis point 
occurs in wrought iron or 
mild or medium carbon 
steel, and is usually well 
marked. With hard steel, 
bronze, and most alloys it 
is non-existent, the rate of 
extension with load in- 
creasing after the elastic limit without any 
sudden jump. 

For commercial testing the yield stress ia 
tho load per unit area at which there is a 
sudden visible increase in tho extension 
between tho gauge marks on the test piece, 
or it may bo taken as tho stress at which the 
beam or indicator distinctly drops when tho 
load ia applied at a uniform rate. 

The author prefers to record that " there 
was no yield paint" in cases where these 
conditions are not observed, but, as same 
specifications require an arbitrary yield point, 
' it is taken at tho point at which the test 
piece extends approximately 1/200 of tho 
giuigo length. With a 2-inch gauge length 
this, for practical purposes, is tho _ point 
where the dividers, when set at 2 inches, 
just fail to " feel " the gauge mark. 

Johnson 1 proposes that " in view of the 
difficulty of determining tho true clastic 
limit- an apparent elastic limit bo taken as the 
point on the stress strain diagram at which 
' tho rate of deformation is BO pot cent greater 
than it is at the origin. Under this definition 
'tho apparent elastic limit would practically 
correspond to the yield point in materials 
having such a point and would give a reason- 
able value for such materials fis cast iron, or 
hard steel, for which this diagram shows a 
1 Materials of Construction, 1918 edition, p. 10. 



very gradual curvature away from the straight 
lino. "Sueh a criterion has much merit ami 
would accomplish tho following results: 

"(i.) It would always fix one and tho same 
wL'll-delinud point. 

" <ii.) This point would always correspond to 
so small a permanent cle formation us lo be, for 
many practical purposes, the true elastic limit. 

"(iii.) It is equally applicable to all kinds 
of tests, whether on specimens or on finished 
members or structures, where deformations 
of any kind can bo correctly monaural. 

" While the iiO per cent increase in the rate 
of deformation is purely arbitrary, it is not 
large enough to fix a point having an appreci- 
able permanent sot, but it is largo enough lo 
fix n well-defined point on the stress strain 
diagram." 

ITnwin, 2 however, aaya that " such a point 
has no significance," also "that tho attempt 
sometimes made to define arbitrarily a yield 
point for materials which have no distinct 
yield point, and, often us manufactured, no 
elastic limit cither, appears to him to bo 
useless mid misleading." , 




It is convenient, where a considerable 
amount of testing baa to bo dime on the smmu 
si/.o of test piece, to use- a simplified exten- 
sion, measurer applied to Iho test piece instead 
of dividers. G. 11. Roberta 3 describes and 
illustrates an instrument of this kind in which 
tho ox tension of the test piece is communicated 
to the pointer on a dial. One division on tho 
dial indicates a, movement between tho jaws 
of 0-001 inch. The yield point is seen 
quite definitely if it occurs, or the load for an 
extension of 1/200 of the gauge length omi bo 
also noted with fair accuracy. 

Capp's 1 multiplying dividers answer tho 
same purpose. They are illustrated in Fig. 
49, mid consist of two arms so pivoted that tho 
motion of tho points in which the short arms 
terminate is multiplied about ten times at 
the scale and pointer forming tho curia ef the 
long arms. To use the instrument the points 
of tho dividers are placed in tho centre punch 
marks on the teat piece and held firmly in 
place when tho load is applied. The. pointer 
moves across the scale slowly until the yield 
point, when a sudden and marked inci'enso in 
the rate is observed. 

(22) THE MAXIMUM LOAD. An mitographirj 

3 Tenting Materials of Construction, 1010 edition, 
p. 206. . ,. 

3 " Enfilneorlng Hescnrch," Inst, , Meat. IMJ. 
Proc., July 1013. , 

* Proc. Amer. Sue. Test. Mat., 191)7, vil. 024. 



144 



ELASTIC CONSTANTS 



40 30 20 



stress strain diagram shows that, with a test 
bar which "necks" before fracture, tho actual 
load necessary to break the tost piece at the 
neck is less than the maximum load on the 
bar before the reduction of area takes place. 
Nevertheless, the stress obtained by dividing 
the breaking load by the reduced area is 
greater than the stress obtained by dividing 
tho maximum load by the original area of 
the biir, which is the figure required by 
specifications. 

Tho terms breaking stress, maximum 
stress, and ultimate stress aro applied indis- 
criminately to indicate tho maximum load 
divided by the original area winch is desired 
by specifications. It is obviously not tho 
maximum -stress, although it is calculated 
from the maximum load. As the term 
breaking stress in also liable to bo mis- 
understood tho author prefers to call it the 
nUitnulc slreis. 

(23) J.'KUOKNTAUK ELONGATION AND CON- 
TUACTION Ob' AitKA. In specifications tlio 
elongation and contraction of area are re- 
quired in order to obtain a measure of the 
ductility of tho material. Both aro em- 
pirical values, and the former, 
as has been shown in (17), 
is dependent on the cross- 
section of tho teat bat' and 
tho gauge length. It has 
been suggested that (ho per- 
centage general extension instead of the per- 
centage totnl extension should bo adopted, 
as this is independent of the form of 
tost bar. It would, however, complicate 
tho calculation of the results, and owing 
to the general adoption of tho other method 
of expression would doubtlessly cause con- 
siderable confusion. 

Tho general extension, if it is required, is 
obtained either 

(i.) J'Yom an autographic diagram, aa the 
extension at maximum load, i.e. before the 
necking of tho test pieeo, or 

(ii.) From the measurement of tho elongation 
on two-gauge lengths on tho same test piece. 
Thus if C L ~ elongation on gauge length L 1( 
e s =olongalion on gauge length L a , 
= total local extension, 
B = tho general extension por unit 

length, 
then fijUTii + a, 

and tho general extension per unit length 



. . - -... 

T, - \. ' 
-I '2 J 'J 

e.fj. with a ISO-ton steel, diameter--l-OI)0 inch, 
Extension on 8"~ 2-1(7 inehos (20-(i per cent). 
Extension on 3" -- 1 '32 inches (44--0 per cent). 



'8-3 ft L '~"" ] ' 

_(l'32x8)-(2-:)7x3)_.'Hfi 

"' ""~~H"-B fi" '" () ' b ''> 

i.e. general extension = R = 21 pur cent. 

(24) MMASOIUNCJ TIIK EXTENSION. The 
gauge length in ordinary commercial testing 
is marked on tho bar before it is tested, by 




means of either a double centre punch (A'j'r/. fiO) 
or tt laying-oil and por cent gango (AY?, 51). 
it id, however, nearly as convenient and almost; 
an quick to nso n jiair of dividnrs HO!) to 
tlio correct flange length. It is necessary to 
havo a vco block to support (be tent pieeo 
during tho nmrking-off process. 

As long as the fracturo is not Icsi than n 
length equal to the square root of tlio area 
insido the gauge mark tho measure o tho 



I, 61. r,ayiii<!-i)lfaml per cent (inline. 

elongation is usually accepted as satisfactory, 
!.fi. 0-fi inch for a test piece of 0-2f> sq. in, area 
or 0-7 inch for a lost pieces of 0-fi sq. in. area. 

Sometimes it is specified that " should a 
tensile test piece break onlwido tbo middlo 
half of its gauge length Ibo test may, at tlio 
contractor's option, be discarded and another 
tensile test shall bo mado from tho same bar, 
billot, sheet, forging or drop forging." The 
middle half is defined an shown in .Z'Vi/. n"2. 

(25) MKTHOD OF KKPOKTINO UUSUJYWJ. It 
is desirable that tlio results should bo reported 

m Bllch , ft ui*a, 

manner that ' ttatf 

tbo infonmu 
lion can be 
assimilated 
as easily as 
possible. It 
adds- greatly 




L^ 


'"'a"" 


L 

'4* 








Qa 


i0a LaitQth 
L * 




1<'I. Bli, 



to the facility with which tho results can I in 
compared and scrutinised if the form of report 
is always in the same stylo. Tho following 
points aro also ivorth consideration : 

(1) Tho report should contain as far as 
possible tho actual observations. 

(2) Tho heads of information which aro 
purely observational and those which havo 
been reduced by calculation should bo kept 
separate. It is convenient to havo tho latter 
on tho right-hand side of tho form. 



ELASTIC -CONSTANTS 



14fi 



A typical fnnn for tensile tests ia given in 
J'Vr/, ii;t, together with (.ho results of a fow 
tests. It in scon that tlio information which 



the hiir (catixl muter tension, a concentration 



roove or notch which in UJIIH formed, while 



T. TUNKILI; TEST OF MATERIAL CAHKIBD OUT ON HOTLHII I'LATK fuim.iKD ny 

A. JtltOWN & Co., L'l'l)., FOU WHOM THK TESTS WBIIK MADE 







OrWi 


il Din 


iii sim IB 




rf 


nil 


on al on n 


nt l'ia 


CIUTO. 








i 






9 




















' f^ 






^ 




o 


'iU 


d 






'S 


J 




a 






t;" 






~ H 








































JJ 


3| 


tt 


^ 


B^ 


11 


H 


a '3 


^ 


"~" 


" 2 3 


H^ 




Haniuks. 




3 


S'H 






f 


1 




iJ !* 


B 




ph 


"H 


W 










6 


a 






a 


w 


5 C rt 

to 


S 






C 




M 




iaoi 


UNI 


9 


5113 


-2189 


3.1 


U7 


07 


1-0 


BOB 


im 


13.7 


3B-10 


.3, 


GO.H 


1 [i'atttlt'u 


1202 


UK2 


1! 


das 


2480 


3-8 


7.18 


03 


1-1 


-380 


1131 


ir,.it 


S8.8B 


81-0 


61.1 




1203 


UK!) 


2 


803 


a-189 


!<) 


0.77 


02 


M 


370 


1075 


KM 


,7.20 


81.0 


^ 





ia n Iti mutely rciiuirod is given in the lust five 
eolnmna 

Example of Test Record and Calculation of 
Ite-wlts, 



the shoulders formed liy the groove nrcvcnt 
free elongation of tlio metal. 

Jn a inntwial whioh extends very little, an 
abrupt change of section will lower I ho 



TKNSILK Ti-av OM ROILKH I'LATI: FOB A, HHOWN & Co,, LTII. 
ntiitcrinl rocoivod July 30, 10^0 





1. 


2_ 


It. 


'l.'u.Ht l\ r O 


1201 






Iilfjiitificiition inni-lss 


UJS1 






(riinjrii louglli 


2" 


, . 




.DinxtiiHioitH of ti\it \mi-M 


0-503" ilium. 






(!i'(iHiJ>Hi!<!ti'iiiul art'ii uf li'Ht jiiceo . 


0-2-I80 sq, in. 


. , 












Yiold Hlri-Hn 






J;!'7 UniH/Mq, in. 










IJIUinivtn Hlri'HH .... 






2(1-10 IdiiH/Hij, ill. 


.l^lnn^iitidii 


0-U7" 


(0-07/3) x 100 


I1S-5 JJIT wiib 


DJHfiimiu (if fnioltiru from giiujju 


1 1 (. 






mark 


1 H> 







])ii]HiriHiiniH at frauluro . 


O'.IDfi" (liuin. 










LM8I)-- -1225 








SJ-180 




liccliiotioii of nrcft ill frnettiro 






fiO'ft |ini'di'iit 








/ JSlifjlitly liiminntml 








\ fnuiliirn 



It will bd noted Unit, with thn fixiii'ntlmi (if Mic orlRlnnl anin, tlin oliwrved vidaiM lire uivtiii In column I mid 
tlui (iiiluulatcil llHiiroH in irdlnmii 3, Tlil iniitliuil simiilitlcs thu typing of thn rnimrt us Klvini In i''i{i. u'A. 

(20) n 1 ' 



' TKNHII,M TIWT UAHS, It is 
shown liy ox|)i)riin(iiit Hint the form of tlio 
teiiHilo tent pioeo has 1111 inflncnco on both tlio 



elongation and tho 

Tho elongation with ordinary teat liurs IN 
ineasnrcd on a #ano length of uniform 
section. The effoot of tho onlnrgnd eiuln IH 
to rodiioo tho loeal drawing-out of the material. 
Tho parallel part of tho tost picuo in therefore 
always made Homowhat greater (him that on 
ivhieh the elongation is ineaaui'ed. IE the 
length of the parallel wedtion is reduced HO 
aa to form an abrupt change in oroHs-Bcotion of 

VOL. I 



nj,! load, while with a diuiliU; inalwial 
(ho stinpi'CHsioii of the liiual drawing - oiib 
gives an inereatitid ton'nilo HlrosH. 
'J'ho inlluiHKio of the gauge length on liio 
o elongation haa been dinwinHiMl in 



On account of tho coiifiideralioiiH Hinted 
aliuve, it is essontial tluili definite types, of 
spiicimen whould bo sneoiliod for eommcroiiil 
IcHts, in which the results of the testa 
decide whether the material iii to bo fie- 
(joptod, 

Aa a roHiilt of the wtivk of liarhn, Ihe I'Yoiiiih 



146 



ELASTIC CONSTANTS 



Commission recommends tho adoption of the 
relation 

oi p L7'2D for circular specimens, 
where L-thc gauge length, 

A area of cross-section, 
D-diameter of the test bar. 
The Gcrmiin Commission recommends the 
use of tho relation 

or Jj = 10l) for circular specimens. 

Thus while, with a test piece 10 mm. 
diameter, a gauge length of 72 mm. is recom- 
mended in France, a length of 100 nun. is 
adopted in Germany. 

Owing to tho practical difficulties in the 
way of adopting a varying gauge length for 
different cross-sections of test piece cut from 
plates and other rolled sections, lixcd standards 
for cylindrical and Hat specimens have been 

< -- B" Parallel -- 

L B" Gauge Length 




Length Pa.allci 



It 


O 


P 


ft 


I 


S 


LI 


L s 


Dl 


D, 


0-977 


J-50 


,1.00 


5 


& 


i-i e.s, iv. 


S'jj 


S 


1-31 


Ji7s 


0'79S 


1 on 


])?! 


i! 


i-5 


1.2 J ft S. IV. 


5' 25 


6'5 


I'D 


I>5 


0.56rt 


S- 00 


2'15 


) 


I.J 


3-15B.S,r. 


-t'2J 


1-1S 


D'75 


l-'fS 


D>JSH 


I'll 


I-SO 
O'SJJ 


1 


J 


o-saa.s.w. 


- 


- 


- 


' 


0-I1S 


0-44 J 


0'H7S 


I-S 


"0"a., 


- 


- 


- 


- 



Radius r should be us laryB as is consistent uiitli 
the other dimensions, 

X These ara B.E-S.A, Test PIcoas 
Slamliird I'onns tit Cylliulricnl Test Dnrs 



prescrihed by tlio American Society for 
Testing Materials (A.S.T.Si.) and the British 
.Engineering Standards Association (H.RS.A.). 
'['ho Bi7.es selected by tho B.E.S.A. aro given 
in 1% fl'i. Those adopted for cylindrical test 
bars of forgings (Fig. M) approximately 
satisfy tho law of similarity, whoro 

L=4s/A, 
vi/.. : 



.Dhunotci 1 . 
InciliPH. 


Arcn In 
Sii. Indies. 


nil (jo LenfitU. 

IllfillCS. 


O-MW 


0-2/10 


2 


0-7D8 


0-fiOO 


3 


0-H77 


()'7r;0 


i 



For platen, both I (Much and H-inch gauge 
lengths were in nso before the li.KS. A. standard 



was published. A standard width of 2 inches 
was used, for convenience in miHinjj; ; this gave 
a cross-sectional area varying with different 
thicknesses of plate, and thus disregarded tho 
effect of the eross-KoeUonal area on the per- 
centage elongation. 

In order to overcome this difficulty tho 
B.E.S.A. standardised tost barn having a fixed 
gauge length of 8 in. and a width varying with 
tho thickness of the plate. Tn order to lessen 
the cost of production, three widths only were 
chosen, viz, : 



Tl licit no as of 


Wiilth of Toil 


Plato. 


liar. 


IlUillCH, 


Indies. 


Under 3 


21 


3 1 I 


2 


Over I 


n 



InclioH. 



(27) EN r. A noun ENI>H on TKS P I' PIKIJKH. 
(J.) Tensile. Tests. Tho design of tho enlarged 
ends of teat pieces requires earn in order to !m 
Hiiro of satisfactory results. It, has already 
been stated that axial alignment of tho test 
piece is necessary for accurate work and that 
this is best attained by the nso of Hpheriealiy 
seated holders. 

For brittle materials it in essotitial that the 
transition from tho parallel part of tho lest 
piece to tho enlarged ends is gradual, ami that 
any part of the enlarged ends whkih IN Hcrewod, 
or otherwise lias a sharp corm?r, in snflickmlly 
largo to prevent fraetni'e .it that pluoe. Forms 
of ends for turned |:cst pieces of cast millennia 
art! given in Fig, fin, 

Teat pieces may bo tapered inside tho gaugo 
length towards tho centre-, to an amount not 
exceeding 0-003 in. for turned test pieces 
and 0-01 in. for sheets or plates, in order 
to induce fraeluro near the centre of the gnugo 
length. ]. thin is done the middle- half of the 
gauge length of tho test piece should bo parallel. 

(ii.) Vumpfeaaioti Teals on Jl lelttlti, With tho 
more plastic metals there iii no well-defined 
point of break-down under compression, and it 




Teat Piece for Wcilgo Grips 
FKt. 05. 

is usual to record the eompressivo strength 
it a given unit of deformation. Tho values 
which are obtained in this way are only 



ELASTIC CONSTANTS 



147 



comparative and do not give results which ran 
bo used as iv basis for calculating sixes of 
structures. 

With brittle materials tlio ultimate stress 
ciin ho ohlainetl with precision, and the 
results fi.ro of value for calculating sizes of 
compression members. 

l''or metals (lie test piece is usually a 
cylinder whoso ratio of length to diameter la 
two. 

Jfc in important, especially with brittle 
materials, that a spherical sealed shackle 
should lio provided in order to adjust for 
inaccuracy of the parallelism of the shackles. 
A form of shackle is shown in Fig, 39. Cam 
should bo exorcised to ensure that the pressure 
is applied axially. 

(28) QUALITY FACTOR. VarioiiH cmpirinfil 
means of estimating the quality of the material 
from the results of the tensile tost have been 
suggested. They combine tho tensile strength 
with either the percentage of elongation or 
percent ago contraction of area at fracture. 
Tho only factor which has been used to any 
largo extent in this country in a modification 
of ono suggested by Wohler: 

Wuhler's quality factor-;;) f. 

and tho modified factor=jH fi, 
whoro ;/)-: tensile strength, 

cpor cent elongation, 
c--)icr cent contraction of area. 

A quality factor must bo used with cure, 
bearing in mind tho HHO to which the material 
Is tn ho put. 

(2il) BUND TUSTS, A rough workshop tost 
of tho ductility of metals is given by tho bond 
tests of various types which aro now in common 
use. Tho test is mado by bending a pioeo of Urn 
material either by steady proHanroor hammer- 
ing, the former giving tho inoro concordant 
results, until an angle- of 1HO is reached or 
previous rupture- takes place. Tn tho latter 
ease the angle is noted at which fracture occurs 
on the ontsido of tho bend. A largo amount 
of experimental work has been carried out by 
Mr. .Hornard h'irth, 1 hut the test has not hccn 
HO carefully standardised as the tonailo test. 

The test in ulno used for ascertaining the 
offuet of punching and drilling on tho ductility, 
by using perforated plate specimens ivith Uio 
holo in tho centre of tho plato. Tho diameter of 
the hole, us recommended by Martens, should 
ho twice tho thickness of tho plato and the 
width of tho specimen livo times its thickness. 

(i)i'J) RINDS oi' 1 .HENH THHT. Tho principal 
typos of hciul test in use arc : 

(i.) Cold bend lost (as received), 
(ii.) Cold bend test (annealed), 

(Hi.) Quench bond test or temper bend test. 

(iv.) Hot bond tost, 
(v.) Nick bond tost. 

1 /ns(, Giv, ling. 1'roc, civ. 25>l. 




Toat/iKj Machine 
(Upper llaatl) 



Test Picon 



(i.) Gold Bend ?'cs(. This is the type which 
is most commonly used and is carried out at 
normal temperature. To test the ductility 
at low temperature- the test pieces are some- 
times cooled artificially. 

(ii.) Annealed Jlr.nd I'e^. Vor tho annealed 
bond lest tho material \K, previously to bending, 
reheated to a temperature exceeding its upper 
critical range, followed by slow cording, The 
steel is usually very bad if it cracks after 
annealing. 

(iii.) Tlif, riui'.nrJt. band teal is used for determin- 
ing tho effect of alternations of high and low 
temperature on the ductility on siich materials 
as boiler-rivet slcel and slay-bolt iron. JJeforo 
applying the bend test the material is heated 
to blond - rod and plunged into water at a 
temperature of 80 ]i\ Tho colour in judged 
indoors in tho shade. 

(iv.) The hot bending test is specified to detect 
red shortness 
or high siil- 
phureontcnt. 
The material 
is bant while 
at a tempera- 
ture of about 
HfiO In 1000 
C. 

(v.) The. 
nif.keA bend 
if, at is in- 
tended to 
show whether 
tho material 
has a crystal- 
line or fibrouN 
H true tn re. 
Tho lest piece 
is nicked nil 

round, before bonding, with a tool having a 
cutting angle of (i(). The depth of the notch 
is 8-10 per cent of tho diameter of the test 
piece, The lest piece should ho placed so that 
tho bend occurs with the minimum depth. 

(31) FOHMS OP Sl'ECIMKSK 1'OH BEND 

TESTS AND MuTimn or' TESTING. Rods are 
usually tested without machining. Plates 
should ho planed at the sides after shearing, 
and tho corners rounded with a file, otherwise 
cracks may start at the corners duo to the 
shearing process having weakened the metal. 
With plates over one inch thick it is especially 
important that this precaution should ho 
taken, 

It is usual to bend bars, unless otherwise 
specified, round a mandrel of a radius equal 
to tho diameter or thickness of tho bar. 

A cold bending apparatus ifl shown in Fii}, fiO, 
in which a steady pressure is applied during 
tho test. Tho lower plate A rests on the 
table of tho testing machine while tho upper 
tool B is hold in place in tho nulling head by 




Testing Machine Tablo 
Fro. 50, 



148 



ELASTIC CONSTANTS 



wing imts (iiul plate. The brackets 00 arc 
spaced sullieirmlly apart to allow the upper 
tool aiul twice; tin! IhiduicNfi {if tlio specimen to 
onaily pass between Iho lower rollers dd, Tlio 
rollora can ))o changed so ua to adapt tlio appar- 
atus for cithor rouml, srjimro, or twisted liars. 

Where a largo number of tests have to he 
carried mil), and llio testing machine or press 
cannot ho Hparnil, it in tismd lo have n special 
maohino used exdimivi-ly for bond, tests, A 
Imnd power maehhjo for specimens up to 
ono inuli square is shown in Fig, 57. 

The correct Hi of centre pin is first put 
in the imiehmo, tlio crunk arm is tinxt, rotated 
until tlio crank arm pin it! bclmv the love! of 
tlio tost piec'e, and then the tuble is adjusted 
by means of the small hand- wheel until tlio 



Worm ami ^ 

(An ttitjiisJuMo gmtltialait rlarj~~~ 
is flxeil to Ilia rcaarsc altle of 
tho Warm-wheel for 
tli6~auQla of bawl} 



JJend tests arc now oflen replaced hy ni J*l*^'~ 
blow notched bar testa (see (08) to S { 1< J1 *^ ' 

but ti.cao require special testing 





(32) TESTS von KIVKTH. Bivnts nr IIHI i 
wubjecslcd to a bend test and a flattening * *' 
For the bend lest they am IminnitJi-ocT * 
without cracking until 1 
two purls of "tlio 
toneh (/-Vflr. 58 (A)) mill J 
tlio flattening tout tlio In*'* 
Hand Wheat auo ?'? l " im "ror| whilo tlio ri \ 
irafit of gottrs foi la ll()t arl(i "Hist (IntU-li Wl4 
^oH/cr ""I cracking of tlio dflj-S'" 1 ' 
a diaiiiolor 2J- tittnf 
the shmik (Wiy. fiS (Ji)>- 



1 ',V 

Hl. 

M 
-1*' 1 



cl 
li- 
*" 



FLANGIKO, ANr) .KI.ATTI-: N I w 

TEHTft l-OR COPI'MH A IN- U 

BRASS TujiE.s. It j.s un I l.v 
specified that bms j 1 1 1 1 
oopper tubes shall Htintfl . 



the diameter {25 pur rc-nt, in 
usual) without orjusk ur tln.\v 
when anbjtictcd to 1m ( 
(Fig. fiO {A}), drifting < 



li in 

U rt~ 

I ( 



l-'ltl. 57. 



top of tlio ftnneimon rcHls against the centra 
pin, which should bo at a-linut Hit) contro of tlio 
mioeiimm. This graduated ring is set lo zero, 
iiiul pnwer in applied to the crank tirin, which 
rovolvca until the lost piece- ruptures or the 
ra[nireil angle <>E bond, rend off on the gradu- 
ated ring, in renehcd. 

A.fiitigiid tost is Homofciincs lined ns an 

altornative to Hie lieiid test. The test piece 

iw placcfl on IJUiiringH with a span of in., 

anil must, nlaiut without fmcturo twenty blows 

fr-oni a weight (of 1120 Urn.) having a rounded 

end of J{ in. radiiifi and falling (I in. Tlio 

',rat jiiotio is to he rovpiwd after tlio first nnd 

vor.v nllonidto blow. The height of full after 

le twenty blmm'sincrrasoit to 12 in. nml tlio 

,i Hi, r'mil.imiiMl until fraotlll'O OOOHI'H. 



-//nut/ W/feo/ ((.!)). Another tiwt whic 

fi-eqiientlyiinpoHcd in Ihil 
ing and doubling ovnr. 
]'H generally carried out I 
cold and at red Iient. 
tiilieiw llattoncd and tjnti 
over tbrongli IfJO" UH nil' 
at /'?>/. fi() ( I)). 

(31) DniFriNfi T.KST OF Mu r rAF,H.- Am 
workshop test for iluotility, which \n njjj 
ordinary shop applijineoa, is to buns li 






A. Bulging Test E' Drlftine Test 

180 

E 

D. Flattening & Doubling 
C. FlanglngTcst '"over 

FlO. 50. 

of a given diameter near to the odgo uf 
plate and open tlmui by ineaiia of a 



ELASTIC CONSTANTS 



149 



drift (taper 1 in 10) until {.snicking occurs 
or 11 definite inereiiKo in diameter is reaehed. 
Tho hole, is usually -*- indi diameter and 1 ! 2 
inch from the edge of the plate. 

Tho following table, givua comparative 
figures for various sines of plate : 

TAIU, i; fj 



Material. 


Thick- 
ness, 
lm:ln;s. 


Original Slstis 
of Mull!, in 
-Inehus. 


Of JlollibcWl! 


Wroiijdit I 








iron j 








(J 


(\--2l\ 


O-fiiii 


]!!() 





o-:to 


O-liiii 


Mia 


MildtilOL'l 




(nun 


i -r>o 



(:!;">) KALI.INII WKKIIIT TKST (eidled " drop 
teat" in U.S. A,).- Tim falling weight test is 
considered (o ho a most useful tost for rails 
and is given a prominent plaeo in rait sjioisi- 
(ioationH. It is made liy planing a pioeo of (ho 
rail 'I to li ft. long on Hii|i]>orla It ft. apart and 
dropping a heavy hainmer, through varying 
di.slaiiues, on tu it at l,ho mid-point of (lie 



fall, nidiim of strilung faces and siijipm'ls, ami 
form of'foumlalion must IIP s|ieeifi(!d. 'l.'liero 
is a dill'ei'entio of ojiinion Jiowisvei- on (liifi |iuint, 
more cKpceiidly in regard fo the foundation of 
tho nniehine. 

I'fti'tiniiliii'.i of tho Hlaiidurd machiuon nainilly 
ndr)|)ted in tho United Stales of America nnd 
hi CJi'unt Jirilain are given in Tallin (i. 

The atinosjiliei-io toinjieriluro in iisinilly 
rcporlcd, and dim allowance is made for rails 
tested at or be!ow (!. 

Tim fulling weiglit test is nl.'io a|i|>lii?d to 
tyivN and axles, h'or tyres aweiht of 2LM01I)H. 
ia allowed to fall freely from 10, 1/J, 20ft,, mid 
npwiii'ds mi thci tread ; the lyixi lining plnred 
in its rniniing position ii]ion n heavy east-irmi 
anvil anpporUid liy n I'igid nimornfe f<mridnti(ii. 
Tho tyre must dulloofc a given amount ivithont 



fraotiii'e. 



lid-- internal diametorof tyre, as rolled, 

in inches, 

(- UiicltiKSHs of the- mitre of tho ( read, 
aa rolletl, in inelien, 



where c, ------ a ei instant depending on the break ing 



.l''ulliii({ weight 




Kii[i|)(ii'tH foi 1 ti'nL |iiemi (anvil dicnj 



iron tNi.iliiiH 15 in. ihinl; ninl 



Anvil f<ii|)|iorl<>il <m '.'.(] 
nri'un^i'd in groups of live 
(luriirr. Tliii H]irii 



I'ieni'H of Htccl having n (lyliiiilrion' 
lii'ai'inj; iiinlaue of Ti in, 

A (ripping di'viiic. 



Mi mt. ft. 

Anvil iiii]i|]i)rlnl dirciit on iifi 
I onii (if iKinoretn ImviiiH an 
aim of 100 (|, ft, Kn liinbi'i' 
iir Hjii'inf'H lirhiwn HID teHt. 
]nct!D mid found 11 1 inn. 



Bpan. Tim rewiilfs nhow if Ihe mil in brittle and 
tho dolleiition (dves a meamire of flio diietility. 

I 1 . II. Dmlldy 1 of U.K.A. irnyti : "Tho |ih.VHJiil 
liroportiuH of dilVerent neislioiiM enn bo oom- 
parod and their lihoniieal eompoHilionnadjiiBled 
from tho reaultft obtained oil tho Htaildard 
drop- touting maehine," 

Tho rcHiiltw iiro (innipuraliv(i only when 
carried out under Mm sninio ooiiditionw. 

It JH generally roooguiHod that the wiidit 
of tup, dintuneo apai'L of mipporlfi, heiglit of 
1 Vroo, Amcr, Sue, Trsl, Mul,, HU(l, x, ail'.!. 



12-IH 
fiO./ifi 



(IK!) Ditin 1 TIWT np TVHKS. Tyres urn 

mibjeetod lo a drop lest IIH well an to a fall- 
ing weight lesl. Tho tyro in allowed to drop 



IfiO 



ELASTIC CONSTANTS 



frr-dy, in n I'liiining position from a specified 
height, upon a mil faHienod to mi iron hlouk 
of not loss than two tons weight, 'I'ho tyre 
is Ihoii turned through 1)0 mid dropped a 
second time. The Insight of fall (lopcm-is upon 
Iho ditimoter (if ('lie tyro (sue Table H), 

TAIN. I! 8 



llclelit, of h'ull In 

1'Vi-L 


illltlil'ilill lllailUil.Or Of TjTl! 

hi Ki'ist. 


fi 
4 

a* 

3 


Up to HJ 

HJ to 14 

4 to 4 
M to (U 


21 


Over (U 



!j (37) TiiM'i'iNU CAM limn, (i.) Traii-tvcrsc 
'l\>xl, -(hvmg In Ilio onse with wliioh it oun l>o 
earned (Hit Hit! Imiisvtsrso, or turns- break iny 
iHt, 1ms heeii universally adopted us tins 
(itiindartl fur cant iron. Tlio tcwt is carried out 

TAJlFiU I) 

PAHTI(]U1,A11H 01.' S'l'ANllARJJ TEST liAHS 
FOK CjAST IllOK 





Kimlitth 
Htinulunl. 


A n 10 rl nil n 
tftnmliml. 


liV diam. 
2CJ 


Cross -Hcoli 01 mf | 
bni'in inoli( > . u i\ 
Longth i>f bar \ 
in inohi-'H 1 


2" ilucji i 
<10 


Ifdiinn. 
15 


Span in inoliog. 
31ow caHt . 


30 
On fdgo 


12 

Vortioally 


23-02 
HoriKtniUilly 



by breaking Iho to.st bai 1 aa a beam loaded 
uontmlly. Tliu strongLh is nioiiaurcd by tlio 
centre load ivliioh tlio bar will carry. TJio 



.1 



ill order to obtain comparative rcsuliH* 
unfortunately tho standards which ti-ro '"' " : ' l! 
in various countries arc ilifleretit. ParL-i* 7 ' 1 ' " 
are given in Table 9. 

The general experienec, in casting 1 > a * J ' rl \* 
the various standards in use, is that |.li* ! 
a little more difficulty in obtaining *' 
bars cast to the English section than i* : 
VIWB of either the American or German 1 " 

^faehined Inirs are goiiorally \vcakoi' 
immacbined apoeimons. ' 

If W is tho central load, L tho spun, ** 
modulus of tho section, and / tho Bl.r<-- ! 
the bar. 

Then within tho elastic limit, 



WL 



-- - = x 



4 



il ' *>' 
i - ii(-u> 



Above tho elastic limit tlio sirens tntl5i' tt*-t 
from tho formula varies for the aiimc miii'* 1 ' 
with the form of the section, but if tlio 1 Ji"<"i> 
ing loitd 1V, ( is suhstitutetl for W, it VJil 
of / is oblaiiKiil wliieh is a measure t*t 
(niality of tlio material for liars of n 
section, and i-s ealled tho modulus of i'uj j 
0. Uailston, 3 in LOU, as a result of n 
of experiments on cast iron ivhon LnfU- 
cross Iirealung, Jiiuls thnt wlioroart tin* 
of tho breaking loads for I x 2 x ItO" (n 
and ] xl x!2" {s]>iin) beams is I-Sflll if 
formula W x L/4 /S! is taken OH applying n 
tho point of rupture, tho actual viihio in I. I 
the pieces arc machined, and 1-1 'IB when I c 
with tho slcin left on. Ho further fine I H 
tho best tent bar to give tho most eoMHfut r^iil 
and comparable results, both with lr*'i*-ltiii|.? 
toad and deflection, is 2&xlj|x42" tuMt mi 
the Hat and machined ilowii to 2 x 1" anil M..- H 1 1 * 1 1 



J 



< 



TAHI.TI 10 

A (JOJll'.VltlSON OF Tin) UlJSUL'l'S ON (llll-JY OAST lllON 

) wing di'urriiW! of the imiihilus of nipturo as tint BJMIII iaorcnaes 



Hiii.'Dii, 
i.'ui'Oisjit. 


Hfian. 
Inches. 


Jili-uii (Joiitro 

J.(IiHl. 

].1).S. 


Modulus of 
]!ii[itiin\ 
I,bf,,/Hi[. In. 

SM. 


Tensile iStretiBlli. 
Lbs./Hci. In. 
S/. 


W-,. 
Hi 


f 


12 


ilOOO 


47,100 


1 


1-Hi 


1-6 


18 


103B 


15,000 


[ 25,000 


1-7H 


I 


24 


1425 


i'1,700 


) 


1-7H 


I 


12 


2000 


4G,BOO 


1 


1-H7 


s-o . 


18 


183Q 


43,200 


Y 24,370 


1-7B 


I 


21 


1205 


110,701) 


1 


i -11:1 


i 


ll! 


2880 


4fi,200 


I 


1 -HM 


2-B > 


18 


1005 


44,900 


}- 24.GGO 


1-H^ 




21 


MOO 


44,000 


J 


1-7M 



clr-lkiftliim in also iitsiiiilly Hjiceified because, 
when fnkcn in ttonjiincMon with tho load, it 
an approximato measure) of tho tough- 
of Iho cast iron. It ifi CHHontial that tho 
form of Uio (eat bar should be standardised 



on a Bptm of 30 in. Tho into of testing Mlic 

not exceed 112 Ibs, in less than 15 s 



1 Scgniiilo acid Robinson, Insl. Oil'. 1'liiff. 
Jsxxvi. 2.18. 
1 tran and Steel Inst. Journ., IflJ-l. 



/ 'rttc. 



ELASTIC CONSTANTS 



151 



Tim reunite in Ttililo 10 of UwlH un grey 
diirtt iron liy Jla thews ' Hlmw that tho inoduliiH 
nf rupture deweasoa as the Kpim merouses ; 
tho (sniHs-Htxtlion being oirmilai. 1 {l.[ hi, diiim.) 
and kept oonstant. 

Table 1.1, compiled from liguros rreonled l>y 
J. K, Stoml," giv(?H a compni'iHon of results 



Tlio following obMirvatimiM have hnon 
recorded us this roHiilt of win-ful experiment, : 

(] ) Square lull's, in .gimeral, exhibit a uliglit-ly 
hihot' modulus of rupture Hum runnel bars oE 
cfi'iml area. Tosts by a cummiU-oo of tho 
American Society nf Jleohanicid Hngiinucjrs a 
give un average of about 5 per cent higher. 



TAIII.E II 

Kxl'KLHMKNTS ON TllANSVEHSM Sl'llEKOTIt 

of tcntn oil IjiigKtth, (idi'innii, niul Aincriciin Hlnndnrd liars 



])<.-!UTiptlun. 


illl'llt'S. 


I mi lu-s. 


Inglinh Hlnmlanl 






('ant (in Hat . 


1-07x1 -OS 


30 


iermun Klniulnril - 






<'anl lioriwmtnl 


1-14 (liain. 


211 -02 


\iiiorionn Klniulurd 






Caul visrtkml . 


l-2'I dia.m. 


12 


''.ii^l isli .Slamlai'il 
(!asl on pilgtt 


1-02x2-0-1 


30 


lui'iniin Klimdiml 






On Hi lioriv-.ontu] 


1-23 (limn. 


23-02 


(,'iiHt vi-r(.ii;nl . 


1-25 (Main. 


12 



LojLd. 



;U<m. 


lloihili'.H u( 


lt-ll]ltlllT. 


olii'a. 


.!,)). /Si|. hi. 


Tou^n.i 


-:iti 


30,/ini) 


Hi-S 


-32 


-10,200 


22-0 


11. 


51,800 


2:1.1 


-10 


42,1)00 


10-2 


)-3(i 


B3,7flO 


24--0 


M3B 


fi2,aoi> 


5S-S 



nblaiiiiiit <m llritiwli, Anioriiiiin, and 
Htiiiidanl liai'H. ,lfin woimliiHion in tluit it ia 
dc-sirablo that any bar for tdHtin^ for (UsdeiiUon 
by tratiH vorwit strciHH Hliuukl not bo ICHS tliau 
24 in. long, us, with HhtrLi)r burs Mian thin, it 
in very ilifllunll. to moaHiiro to tint i-wpiircd 
degree -of neeiiraoy oxisent with very delicate 



In commoroial work 11 dofimjtometw of the 
typo Hhown in Fi{j. 00 in 
gcnemlly iiHtid. It consiHtn 
of a cuHt - iron huso the 
buttoni of wliiofi ifi Bttro- 
fully jilaiuid. This base 
Scale r oftrrica a salo alnng which 

tt levc-r niuvea a vernier 
reading to 0-001 in. Tho 

Sliding 
Vaenier 



28-10 
1210 
3230 

3.170 
10(10 
3380 



(2) .liars east horizontally nnsHfron^H 
tho loud in applied a^nhiHl. tho ciopo fiu'<;, 

(3) .Uoii^h biu'H arc Htroiigiir lluui iiltincd 
burs,' 1 

('!) TunibliiiK in a rattler imminscH, UHI ImnS- 
nc3H of tho Hlviu mid thoreforo jinpnmm Iho 
Btrongtli. 

(ft)' Tiara run with hot moiul urn wonluM and 
dclleot inoro thtiu barn run with dull nieliil/ 1 

(0) Tapping n biu' with A hummer during 
tost rctlnees ifs strongth." 

(7) .Fur bars of tho fiiimo jirnporticniH, 
tho inoiluhiH of rupture ifl Jcnvor as UHI 
aeotiim is largoi 1 . 




FlO. 00. 



ndjnsting screw of the lovor is arranged under 
tho transverflo tool an as not to bo nffcctad 
l)y tho bi-oaUiiiff of tlio 8]woimon. A Hhiiplo 
nnungomcnt which is sometimes adopted 
to HBO a Brown and Sharp lalho indicator 
under tlio transverse tool at tho centre- of 
tho beam. 

' I'roc. Amer. floe. Teal. Mat. s.Zm, 
a Proa, Int. Aasoc, Test. Mat,, 1012, vi, !- 



(8) A wide hr givoa a liighcr, find a docp 

bar a Inwor modulus of niptnro, 8 
With tho English standard tftsfc pieces 

3 Trans. Amer. floe. Mech. Kay, xvl. 5-13 (iml 10(1(1, 
anil .Uolihison, lust, Oiv. Kna. J'wc. 



J. 248. ,,,-,, , in nan 

Millar, Inst. Civ. Huff. J'rac. Ivlll. 322. 
'Unwin, Teslinf/df Materttils of Construction, ll 

cd., l). 291. 



]fi2 



ELASTIC CONSTANTS 



(I" \vidf, 2" clwip, 43" long, and ,'[(" span) tho 
(strength of oust iron ift ustmlly specified by its 
breaking load in i;\\ts., figures of 18, 28,' and 
38 {cvts.) corresponding to poor, fair, and 
good oust inm. A usual specification is that 
the cast iron shall sustain a load of 30 owls, nt 
the centre wJlli 11 clofloclioii of not less than 
3 in. 

A form of roporb which is suitable fur 
transverse tests is given in ffiij, (il. It 



*' 1 ll!< 
J i<|m * 



tsiist iron to oiiHiiro that tho ]nil| | H nxi 

tliis material is greatly weakened \>y *> J 

or eccentric loading. ' For aceinutn ( f 

shackles with spherical scats should >*" 

ployed (sou Jfiys. 33 and III), L.I it' 

bar should bo oust in one with fch'o wc>H J ""' 

turned to a suitable si/u, care boiii" 

avoid mj)id oliangos of seetinn nri\- 

of tho spetsiineii under tost. 

Tlio HI/.O of (jio liar from whicli 



11 ln 
l" ir(j 



Supplied bj 


teaU of Millennia ciirriud out on 






Deflectinn at f =~ 
Fracture in Indies.! 2 


tlio tosl-a wer*' 




_ 




2 


2 f 

S !i 


III 

g g- a 
P 


lll,,, n ,,.|p,i.. 


o 


[.nfl^t 


it re ii 

if 

o 

a 


S 

u 

P 


h 
u 


1 


J.g 

.5 ^ 
3 a 


Ho rim r It ii. 


3 r' 





u 


6 


it 
W 














Order No. 
Reforcnuo. ,. 



enables the salient points of tho results t 
bo seen lit a glaiuse, and moota all (irdintuy ease 
on tho tosting of oust iron. 

(ii.) EJfecl of Temperature on the 'franvvers 
IStrenytJi ,>f Cast Iran. CJnst iron loses very 
little of Hs strength or toughness up to i 
temperature of 400 C. Tho following sets of 
oxperinu-ntal rcaulls ]jy Moyor ' show tills 
very clearly. 

TABLE 12 



I TimijK' ru turn. 


AhLlulMnf 


Jinx Iran in 


1'. 


'L'onii/.S(|. In. 


inches. 


18 


2,'{-r> 


0-31 


Ijfl 


23.2 


0-30 


2(i3 


21-1 


y.i>g 


297 


111-fl 


0'30 


fi'20 


12. 1 


0-Bfi 


B07 


7-6 


0-0 '1 


18 


23.fi 


0-30 


8S 


21 .0 


0-28 


lofl 


21-3 


0-28 


370 


21.0 


0-30 


fiHO ' 


Hi-0 




810 


(i-2 


0-70 


(38) 'l.'[jN.sjr,i.: STHKMTII oi 1 OAST IKON. 


t is jinpni'tmit wlioii making lonwlo tents 'on 


Staltl will Kinfn. xvvl. 1270-71. 



c.f 
in 



pieco is taken au'cets tho results <d>l 

bars of larger section giving, as a nil,., town 

results. 

Tables 13 and 14 give results rcxHirrlttc t liv 
f. K Stead a on teat pieces prejmml m nil 
bars o various n\xon which have bnun onwl, in 
dift'oi'ont ways. 

Tablo 10 gives results obtained by Aln(,lu*wji :| 
on east iron crjiitnining various ]>minlai *,.. .if 
silicon. "" 

A eomjiarison between tho tnoduliiH 
rupturo and tho tensile strontrth ia iriv^'i 
:i'ablo Ifi. (1 

(39) CiiusiriHa STIHWOTH OF GAHT TKO 3sr. ^ - . 
The oriishing strength of east iron in obi nitt^rl 
(in cylinders or prisms in which tlio infi< of 
tho height to tho least lateral dinuimJoii IK 
between one and three. 

t Tho crushing strength is usually ubmit Itvn 
times tho ultimate tenailo strews, and H)*j]ir]* M 
of bad, good, and very good east iron H!LCIU Iti 
givo a crushing ntrcsa of 30, 40, and fiO ttttm 
per sqimre inch respectively. 
(40) RESISTANCE OP CAST Tnos TO T>nti-:<i'i< 

SltEAIt ANO TOHSIOHAL SlIEAR. As tlm IVHItli 

>t experiments in direct shear by Pint I, 
Kuywai-d i it was thonglit that tho H!UU 
strength of east iron was about fivo to nix I,CJH H 

ior sqimro inch. T-/.od, 5 however, by UH!II K 

3 J'foc. Int. Asms. Test. Mat., 1912. vl. 4. 

rroe, Amer, Sac, Tent. Mat. x. 200. 
fnsl. Civ. ttna. Proc. xc. 382. 

fnsl, Mecfi. Kng, Proa,, Jan. 1000, 



ELASTIC CONSTANTS 



mom ppiTi'ot apparatus, has obtained much 
higher figures, and UK.'HO are confirmed by 
Goodman. The rcaiilts of these lewis, together 
with tho figures obtained from gun-motivl mid 



Hiving a lower rc.sult in jihoiu- than in 
tension. 

Fremont is of opinion that the shear test 
gives a very useful indication of the quality 



TADLB 13 

TENSILE TESTS m; OAST liiou 
Teat pieces 0-71)8 in. diami'tiy, O-flOO H(|. in. area 



Description, 


No. of 
Testa. 


Ultl inn to 
fttivss. 
Tons/Mil. In. 


Avorase pm'cent 
Variation from 
Average. 


HmnarliH. 


CiiHt on Hat in biirs 2x1" 


4 


11-2 


1-3 




Cant Imrimntnlly (1-187" diameter) 


4 


12.2 


1-8 


-All test jifaoefl (iirnoil. 


Oust vertically (l.|* diameter) 


4 


12-2 


1-8 


J 



TABLE U 

TENSILE TESTS ON CAST luos 
Tost piccca 0-798" diameter, 0-;"iOO sq. in. area 





No. of 
Teats. 


Ultimate 
Tons/Sq. In. 






Variation from 
Average. 


Cast horizontally as a tost bar (!.[" 
diameter) 


}< 


13-9 


0-9 


Tested with skin on. 


Cast hori/.onlally (1-187" diameter) 


G 


134 


3-2 


Tiinunl to 0'7(lfi"dinmofor. 


Cast vertically (1-187" diameter) . 


G 


J3-5 


1-8 


Turned to 0- 708* diameter. 



Only tent plcisea wliieli broko with a wmnd fracture are included In Tallies t!) nnd 11. 

TAHLB Ifi 
oi' MODULUS OP RurTuiu; AND TBNSIM-; STRENGTH OF CAST IUON 



Type of Test Bar anil Authority. 


Modulus of [Rupture. 
Tons/fill. In, 
A. 


UlUmate Tensile Stress. 
ToiiM/Hq. In. 
.. 


Hatio. 
A/H. . 


< 


21 '0 


11-4 


1-84 


American Standard (Mathnws) 


20-3 
20-3 


10-i) 
11-0 


]-8fl 
J-8-i 


Ainerioaii Standard. (Stead) . . . 


23-1 
23-3 


12-2 
13-5 


1-89 
1-72 


English Standard (Stead) . . ! 


IC-3 
19'2 


11-2 
13-0 


I -10 
1-38 


Gorman Standard (Stead) 


22^0 
24-0 


12-2 
13-1 


1-80 
1-79 



mild steel, for comparison, tiro given in 
Tablo 10. 

The point oE interest in Tablo 1C ia the fact 
that tlio shearing strength of cast iron is 
higher than tho ultimate- tensile strength. 
Goodman nays that, with the exception of 
specimens which arc defective on account of 
blowholes or sponginess, lie has novor had a 
single instance of a specimen of cast iron 



of cast iron if tho sample tested truly represents 
tho material of tho casting. Me has devined 
a special test for this purpose. 1 A small piece 
of the actual casting, 25 mm, diameters nnd 
20 mm, long, is detached by a trepanning too!. 
The specimen is placed within a block holding 
a fixed blade, and is cut by a movable blade 
which is forcpd into the specimen by a weight 
1 Fremont, Oomptes Rentlus, Dec. 9, 1918. 



154 



ELASTIC CONSTANTS 



acting on 11 lever. The: force of rupture is 
estimated from the weight and leverage. Sinco 
the diameter of the Jmle bored in the casting 
13 only about 1J in. diameter the casting 
is not spoiled by thia method of procedure. 

Under torsional shoni 1 a round bar of cast 
iron invariably fractures along a helix whoso 
angle ia 45, that is to any, it occurs where the 
tensile stress is a maximum, and indicates 
that cast iron has a lower resistance to tension 
than to shearing, . This conclusion confirms 



(i.) Thi MJfnct of Perfnmtion on i/ t< > 
of M-ild f>lael .I'lufai. In tho i][H<: 
a paper by W. .Hackney before iho 
of Civil Engineers, Stromoycr ' d(!Ke 
pcrimonts carried, out to dotorminn l, 
of perforation on tho tc*nail<s Hli-on 
elongation of boiler plates, Tho forin 
bars that he used aro given in Fir/. (j,3 
results are given in T.ahlo 17. 

Tho test pieces iu>o all cut from ,, 
of plate 12 mm. (/) Ihicsk, and tho h 



><" 



TABLE 1(5 

TESTS on CAST TROW 



Mater Inl. 


Ultimate 
Tensile HtrcsH. 
I''/. 


Ultimate 
Sliuur Stress. 


.Itatlo, 

M 


Calculated 
CoefUcient of 
Torsi mini 




Tona/Sq, In. 


Tons/Sq, In. 


l)i 


StrniiRtli. 
Tous/Sfi. In. 


Cnst iron A 


fl-7 


14-8 


l.f>2 




i. i, B 


13-1 


J74 


l-ll 




. . 


11-3 


13.9 


1-23 




D! . 


13.7 


10.1 


1-18 




J) a - . 


13-5 


14.8 


MO 




Cast iron . . . I 


10-0 


12-9 


1-18 




\ 


11-fi 


13-0 


1-13 


10-0 


Giinmetal . . . J 


12-1 
12-4 


12-5 
17.4 


1-03 
I.JO 




( 


13-8 


10-0 


1-1(1 


21-0 


Mild steel . . . / 


20-0 
23 -G 


21.0 
18-9 


0.78 
0-81 





Author Li .V 



Iztwl 



CJoocIninn 
IKOC! 

Goodman 

Issoil 
(Joodmnii 



tho direct slicar results of I^od nnd Goodman 
A typical torsion fracture is shown in Fiy. 02. 



(41) INFLUENCE os 1 FORM ON TJIE I'HOPI;K 
TIES OP MATERIALS. An abrupt eliango in 
tho cross-section of a tensile or transverse test 
bar causes: 

(it) A (limiinition of tho elongation at tho 
redneed section due to the shoulders of llio 
notuh or groove. 

(l>) The stress to ho highly concentrated at 
tho periphery of tho groove or notch. 

There are thus two effects the suppression 
of tho drawing out of the material onuses a 
gain of strength, while- the inequality of the 
stress on the section of fracture gives a re- 
duction in strength. 

With a brittle material, e.g. cast iron, tho 
elongation is negligible, and in consequence 
the effect of a groove is to oauso a reduction 
of strength. On tho contrary, a grooved mild 
steel test piece is stronger than n plain bar of 
the Hume material, because the suppression of 
the drawing out causes an increase in strength 
M'Jiieh is greater than tho effect duo to con- 
centration of stress at tho groove aotin" in 
tho opposite direction. 



all 24 nun. (d) diameter. Tho width (t>) \'JM 
in dift'cirent bars from ?() to D4-0 nun. 

(ii.) Strength of Screwed Bolls. This rc-n 
of some tonsilo tests on fnur dilTnrrnt kint IB 




B 



aorow threads, made by tho autlior, ai-o 
in Table 18. Tho threads selected worn i 

(1) British Standard Fine. 

(2) British Standard Whitworth. 

(3) Sollei-H Thread. 

(4) U.S.A. 00 Sharp Veo Tlironcl. 

Four materials were used, lunci 1 1 \* 
ultimate stress from 24-0 to 52'7 teum'* 
square inch. Tho bolts wore g in, 

1 Proc. Inst, Cir. Eng. t 1884, Ixxvl. l-itJ. 



>>, 



ELASTIC CONSTANTS 



155 



motor and woru all inn<jliin<'<l from IJ-in. ilia- 
jiiotin- Imr. 

.Krom tho results in Table 18 it is seen that 
foi 1 steel up to 40 tons per squaro inch the 



those, soruwert with JJ.S.W. thrctul, arc we 
than tho plain bar. 

Marions 1 has carried out Himilm 1 testa on 
,1-in. and 1-in. bolts, using steels of 27'7 



TAIIU: 17 
STBEHOTK OF PKHFOIIATHD PLATES 



Form. 



1. 


Dimensions. 


HiiUo. 
It 
if 


Elongation per cent. 


Width. 
b nun, 


Thickness. 
( niiu. 


Of Hole. 


In 50 mm. 


In 2(]0niin. 




;ir, 


12 








2CJ 




40-8 


32 


1-94 


50 


20 






31-8 


12 


1-32 


11) 


IS 






18-0 


12 


0'7u 


27.1 


14 






12-6 


12 


().fi2 


21 


12 






6-i-O 


12 


2-25 


54 


28 






44-0 


12 


1-83 


50 


20 






34 -0 


12 


1-42 


40 


22 






28-4 


12 


MS 


4H 


22 






2JJ-3 
18-0 
18-0 


' 12 
Id 
12 


0-97 
0-77 
0-54 


37} 
334 
25 


20 
10 
14 






7-0 


_.. ^ J 


0.32 


21 


10 





Ultimate Stress. 
Kilos pisr sq. nun. 



4-1-0 



} Moan 47-8 



fllenn 4S-7 



18 
TKNSILM TESTS ON J|-INCH DIAM. SCJHTJW HOLTS 





JIfttcrlal. 
A. 


Material, 
I). 


Material. 
(.!. 


Material, 
1). 


Tensile. Test on Material 












I5'0 


17-0 


23'C 


2fl.<t 


Ultimalo stress .... 


24-0 


20>5 


40.3 


62.7 


I'oi 1 cent of cxlunsion L/ \'A<=4 


41 .0 


30^0 


28-0 


10-0 


liritiah Standard Fine TJircad 










(Rout diam. =0-6335 in.) 












17-8 


20. 1 


24-7 


20-7 


Ultimate ulrcsa .... 


20-3 


33'8 


40-0 


48 .0 


British .Stanrlard Wliitwnrlh 










(Unol diam. =0-CU8(i in.) 










Yield Htrras 


is-o 


20 -4 


20 .0 


2Q.O 




27'0 


34.0 


45.1) 


54-0 


Sdloi-B Thrwul 










(Koot diam. ^0-COGO in.) 












10-0 


21 .0 


25.fi 


20-0 


Ullimato stress .... 


2G>8 


34-7 


44-9 


61-0 


U.S.A. Sharp 60 Veo Thread 










(Root (Ham, =0-405 in.) 










Yield stress 


17-7 


21-3 


20.fi 


2fl'G 


Ultiniato stress .... 


28.2 


30-3 


47-1 


47.1 



Note. (1) Stresses arc given In tons per (Kniuru Incli. (2) For tests on threads, the nren for calculating 
tlio stress is lultGii as that at tlio bottom of the thread. 



strength (per square inch of section taken nt 
tli bottom of tho tlimicl) is greater for tlio 
bolts than for the plain bar, but that for tho 
53-ton steol tho bolls, with tlio exception of 



and 23-9 tons per squaro inch respectively. 

His conclusions are as follows : 

(I) Screw threads subjected to plain tension 
1 Zeits. Verr-ines Deutsch. Inn,, April 27, 1811(1. 



ISO 



ELASTIC CONSTANTS 



arc stronger than |ihiin bars of tho aaino not 
cross-sectional aroa, tho excess of strength 
being approximately 14 per cent. 

(2) Them is no marked ditferoneo in the 
ultimate strength with different forms of 
threads tlio sharp thread in slightly Wronger 
than the olhuir!. 

{))) Under ropc.atcfl loads and inipaot it is 
prohablo that tlio sharp veo threads would 
develop craokn ([nicker than the other, forms, 
fiiul that tlio U'hitworth thread would ho the 
last to show this weakness, either with repeated 
loads using soft material or static loads with 
high carbon steul, 

Tlio two seta of experiments, by different 
experimenters, described above arc in agree - 
ment. It will bo HCCII that Martons's siipposi- 
tiou with regard to tlio superiority of the 
B.H.W. thread with high earbon studs under 
static loads is shown by the author's testa to 
bo correct. 

With regard to Martens'H statement of the 
probable weakness of nharj) voo threads under 



in the same terms an \t' 
hut alwayw with bifdirr n : 

On the other hand, I.,-' 
to find, this diO'orviirr v 
testa gave fractnrr-i ),;,- 
appearance in tho lw c,t 
tions of similar- barn \n>n. ' 

(ii.) E/fed of ]><,:,,;,> 
IjOddinff, .liansehiiii'i'r * ' 
complete- set of oxpV'iimrP 
of loading and showed It,,* 

(1) The offoet on th,, ,..! 
the rate of loading vinm' 
material employed. Will" 
was negligible, \iliiln uiM, 
copper, broiue, arid hnivi * 
it was masked by dill'i'i,.,,' 
the test bars. '\f,, r |,, jl( | lt . 
marked inoreaso in (\w .<\l 

(2) The nltima.t(t hr:. 
greater when tho t-x(,. M " 
when it was alow. 

Testa on iron ami ttln-l 



1 1 



TABLE 10 
IMPACT TESTS ON Somsw THHKAIIS 
{1 INCH DrAstETKH) 


Kind of Thread. 


.Dlamotcrat JSoUoin 
of Tlirend, 
Inches. 


* hi l^n'.Vl 

J021 
18HH 
2(HH( 
Jrtdl) 


Jiritish standard fine (H.S.F.) . 
Sullcra thread (chasing tonl) 
Scllora thread (single pointed too!) , 
British standard Whitworth thread . 
U.S.A. sharp vco thread 


0-872 
0-83Q 
0-83B 
0-8-10 
0^780 



impact, some tests by the author also eonfii-m 
this oonoliiflmn. The tests, of whiuli tlio rosultu 
urn given in Table 10, ivoro mudo on 1-in. 
bolls and broken by a single blow, the energy 
absorbed in fracture being measured. It will 
bo noted from tho table that the shurp vco 
bnlta are tho weakest of those tested and tho 
liritish standard threads tho strongest. 

(42) Isiir.UKHaKOJpTii[]sowTsTllKSur/i'a. 
-General oxnorionco shows that elongation 
and contraetiim of aroil am increased by vory 
rapid loading, but that within tho ordinary 
limits of time occupied by a tonsilo test to 
fracture, of most materials, tho into of loadim* 
docs not appear to have any effect on these 
results. Tho results from various experi- 
menters, however, are not quito consistent. 

(') Effect of very llrtpitl Loading. Maitland 1 
found that stool, broken in impact, gave 74 per- 
cent more elongation than tho same material 
broken in the static tensile testing machine, 

-BloLiiit, Kirkaldy, and Rankoy 2 concluded 
that the irnpaot tensile test gave tho ductility 

Ixxxi'/ilir 10 " 1 '"' r1 "" StMl1 " I>lsL Oi "' A '" ffl 1>rac ' 
3 " CoiiiiMji-lson of Jfotlioda of Ti-Htins Steel" 
Insl. Mech. &,. JVoc., May 27, 1910. ' I 



mission des mdthudcn il'l-s , 
show very littlo ditfrivn. -*= 
o.v tension of tho nlf inm( .ti r 
out in a few seeondu nr \n-.\i* 
^HoUiunley,"! bmvnviT, v.Ii 
with soft ii'on win), f ....... I t 

contraetion of area ami li.. ,,, 
loss if tho loads WCIT' nj.j.l 
His researches incbiilnl u 



* B 



Tinui tlio T,oiul wan 

nllnwcfl to mimln on 

tlio Wive. 



Ordinary teat in 10 

2-1 hours at 43 Ibs. . 
84 lioiirs at 43 Ibw. . 
2 months' grachinl 
loading from 40 HK-. 



.1.4 



3 Ann. ties pouts el. t'/mns>,,'f,i | > 
' Inst. Pic. ISng. l>n>n. cvlt. If a 
1 nitHhoiles d'easui tips m/i(.Vi.i-. r ', 
'. Article "Elasticity" In ' . 
Jinlanmca. ' 



ELASTIC CONSTANTS 



in? 



the effect of time on tho breaking loud of soft 
imn wire. Ho found that tho iviro, if liwJccl 
to just Ijolow tho ordinary breaking load, in- 
creased in strength according to tho timo the 
wiro was under tins initial hnul. 

A summary of tho insults arc given in 'Pablo 
20. 

IV. MuAsuiiiNCf TNSTHUMKNTS FOR THK DK- 

TEHMINATION Off THE ELASTIC CONSTANTS 
Of METALS 

In order to obtain information aa to tlio 
ohistie constants of materials it is necessary 
to measure- deformations while those materials 
arc being strained elastically. 

.In commercial testing, where a measure of 
tho ductility only ia required, tiio liniil amount 
of deformation ia all that ia necessary. In a- 
ttmsilo test witli a standard 2 -in. gaiigu 
length and cross-sectional urea of 0-25 sq. 
in., tho total elongation may bo 0-50 in., 
und an this can bo nicasiu-cd by tho aid of 
dividers to tho nearest i -Jg- in. tho accuracy 
of rending ia 2 per cent. 

Using tho same sixo of test piece and gang* 
length, tho extension at tho elastic limit ia of 
tho order of 0'002 in., 'no that for tiie name 
pomsiitago accuracy the measurement nuiflt 
ho correct to 0-00004 in. ; tho smallncss 
n[ tliin extension can ho realised when it ia 
considered that tho thickness of n picoo of 
<; igni'oLto paper -is almul 0-011 1 in. With 
tho heat types of mirror exlonHOiiieh!] 1 , altom- 
tiona of length can ho accurately inetiaurtul to 
-,V of this amount, i.e. 0-00000-1 hi. 

('J3) ExTKNHoMETJ'iiiH. In liny typo of 
Hl.ruiii-iWHisurinjj apparatus there art* eei'tain 
gonoral prinuiplcH which it IH advinublo should 
ba lullillod. 

(i.) IE changes in length of tho nxis of the 
tost bur am to ho determined, miuiHiircinnilH 
slmuld lio talton on o|i|>i>mlo Hides <if tho 
Unwin ' has whowu that, if this 
ni iti not Hiilisfhul, initial cni'vntni'o of 
tho liar will mnisu Hcrioim OITOTH in tho 
vomiltH, but "if Uui miNin of jiioiisiiroinoiils 
taken tit points syimndriwilly platii'd on 
oifchwr sido of tlio har En adopted, thu pri'oi 1 
duo lo oiirvatnro ia noarly (tliniintiliid, (Jio 
luiigthoniiig of tho dinlaii(!(i of ono fiido 
being coinjJoiiHtitcil by sliortonin^ on tho 
otlioi. 1 ." 

{ii.) The apparatus) nhoiild ho dinmtly at- 
tached to tho tofit ])!(; at tho f!ini|j;o jiointn 
<inly t and after tlio initial witting it should not 
ho lusooEjaary to liiuullo it diirinj; (ho eoiir.so of 
tho oxnorimunt. 

(Hi.) The instrument should hi! a.<i li^ht as 
nnaaihlts, and designed HO UH (o bn rapidly 
attaelkcd to or dotnelicd from tho tiwt ioiso 



18S7. 



IiiBtnimiinU UKcd In Mi'rhiinhvil 
," /Vii7. Jl/fltf., Mnrcli IHHV : 1'hns, HIM.- I'rw... 



without iiitei'foring 1 with tho application of Clio 
load. It is advisable that, if possible, :it HlimiM 
bo self-contained. 

(iv.) 'J'ho inatru merit flhould ho a.JTimg<vl no 
that its ncouruoy can bo dcterinined \iy n 
calibrating device, and tlio attachment let tlio 
test pieecj sliould be mieh that tho f;ango 
ia cajiablo tif dotormination -with 
accuracy. 

(v.) Tlio mechanical or optical details, and 
tho relative positions f all tlio purls \vifh 
respect to tho axis of tho specimen, nboulit Im 
such that tlio "constant" uf the insirinnotil 
ia tlio same throughout its 3'juigt', or that any 
errors which aro involved nro BO ainall as to 
bo of no importance. 

(vi.) Tim zero of tho instrument should ho 
constant for tho samo cimditinns of test ; tlnm 
if, after straining the tcfifc piece, there is no 
pernmnont set the instrument should return 
to its initial position. 

Extensions are measured in live tiillonmfc 
ways : 

(i.) With a mieroinolor serow. 

(ii.) By an indicating dial, 

(iii.) With a iiiiorosoopo. 

(iv.) ,l!y 11 ]iHiltl]ilyiiiif li-vef (mechaiiioal 
]nii).;nilk;alum). 

(v.) Uy optical inagniiication. 

AVit.h methodri (i.), (ii.), ami (iii.) the dcforma- 
tiinui in'onscortaincd with litUuorno inii^iiilicn- 



(iv.)and (v.) tlioj slra inn arc t 
liinl bdf{)]'<; the iiicasniMMiK'iits aro inndo. Hinun 
oxluiiHiniKit.er.'i UHii a- wuiibiiiiition of (i\ r .) or(v.) 
with (i.), (ii.), or (iii.). 

g('M) JllDHOftlKTMlt HOHI'.W HXTKNWOniU'L'l-:!!. 
..... 'I'llCMO illHtniUICIltH IlOMBiBly of tU'H (tlltril])!! 

placed on the tent bar at a dmtanco a|mrl< 
whiish in eipnil to tho KRII^D lengtli, Tlio 
movonitnit of ono clamp rcliitivirly ID thu oHiri 1 , 
UH tho load is a])|)]iod, is ineiiHunnl hy (fin 
I'fliuHng of nno or mure iiHuronititni 1 Koro\ni 
fixed to nno clump and brought into emitim!, 
with llni otlHsr. The aecnraey (| f tho iiuttnt- 
iiKint depends on ; 

(n) Tho uniformity of tho pitch of tlu< 
miemmotor HISIISW. 

{/)) Tho constancy nf tlio ni-cusuro at Mi" 
point of eontntit. 

(i;) Tho caro with whiivli tlio ijiiisronii'ti'i' 
Horow i:i o])0i'4ito(l, heiniUKii |.|m iiml.ritiiit'iit him 
to 1m touched by hand many MIIII-H ilm-ing ih 
experinuiiit. (.'are Hhixild bii tibHorvnd in mdiT 
to oiiHiii'o that Iho (toiiplo ii|i|)lii;d hy (hn 
(in^eE'H )H jKTpenilicidar to the a.\is <if lint 
no row, 

Micrometer fsennv exti'iiNiHnotci'H iiro luij^oly 
iiHi-d in the U.S.A. by HtudontH, and \f\vti 
HiitiHfantnry I'dHiiltii when iiHtul willi gi'i'iit run-, 
Tlio principal uialu'H of iiiHtrnnu'iit nn> dividfil 
inli) two Koctionn itcoiii'ditut tin to whniluT lln\v 
lutve ono or twn ini 



Ifi8 



BLAfiTtC CONSTANTS 



(45) DOUTII.E JriunOMKTKK SC!HK\V IK- 

STiiiJfliKNTS. (i.) Prafexsor it. If, Thiirslon's 1 
Kxt&nsometer (1S75). This was llio first in- 
strument in which two micromotor screws 
wore used, DUO plnml on each sido of iho axis 
of tlic test pieno, nnd in which clentrio contact 
was enii>loyc(l in order to eliminate errors duo 
to variation of pressure. 

(ii.) Hennhiijs a Micrometer .Kxlcnsameler. 
This instrument is sliown in Vitj, fi-i. Two 
frames A a-nd JJ grip tho teat picea liy two 
steel points h, h imtl two knifo edges c, e. 
Tlio lower frame ]i carries two im'uromotora 
wi, m, (ind the upper frame A is provided 
with a pair of plugs;/, p which itro in lino with 
the micromotors. As tlio distance between 
the frames increases with application of tho 
load, tho ends of tlio screws /,/ are brought in 
contact with the plugs g, g, T.ho contact is 
indicated by ringing an electric boll by n wealc 
electric current, or, owing to tlio uncertainty 
of bell mechanisms, telephone receivers are 



i MI 



,r,, 
of ( 



*>"*" J l ' 11 ' 
M' - 




nti|> 



I'll!. fl.J. 

sometimes substituted, Tho extension is read 
on vortical scales e, e nnd the gnwluiiliona of 
tho micrometer heads HI, m. 

Tho instrument registers to one ton- 
thousandth part of tin inch, and can bo used 
on cither round, flat, m 1 square specimens, In 
order to attach the oxlensomotor to thu test 
piece, Hie frames A and H aro ojioned. Uni-a 
d are used for Retting the finmcs A and Ji 
at tho correct dinKmco apart; they arc removed 
while tho teat ia in progress, An instrument 
of this typo is supplied by Messrs. Tinina 
Olaon Testing Machine Co., Philiidolpliia, under 
tho imino of Tho Olaon Standard Duplex 
llidroinotor oxtonsomctor, 

(iii.) The oxtoiisoniotor invented by 0. A. 
arnrslifdl, of thn Cambria. Iron C'onipnny, differs 
from Honning's in three small details. The 
adjusting bars d (Fig. 04) aro omitted and 
the liiiifo edges o, e. aro replaced by a spring 
and roller attachment which, in connection 
with a spirit level, assists in tho accuracy of 
tho adjiiBtment. Tho mioronieter screws aro 

' Materials of Engineering, \\.<m, 
'Jrans. Amur. fiae. Mecit, Eng,, 1885, p, J70. 



placed nearer tbo lower frame fl '' <1 " 

Honning oxtcnsoinoter. 

(iv,) The Ynle extensonieter 3 is 
li<in of tho Marshall apparatus'. 
n.H.,1-8 are omitted mid a gauge bar in I 
to keep the clumps parallel, briim (In 
of measurement opposite, t tnd ' 
length. '.I'he gauge bars are made 
lengths and are removed before 
strain the specimen. It 
roads to ton -thousand the [~| 
of AH inch |,y micrometoi 
screw. 
(40) SiNtiL!-; MTOHO- 

MliTHK SlIHKW I-NSTIUI- 

MKMT. Vnwin's * Screw 

strnment is shown din- 
grammatically in 7<Vf/. OC. 
Tlio two frames ai-e 
clamped to the test piece 
at points on u piano pasn- 
ing through its axis by sot 
screws ami li. 'The 

.Lilt, , ,, ,,, ,,,,, 

lower frame carries tho 

micrometer sorow e, on the hardened |Mtin( "t 
which the upper frame rests. Provide*" I Mml 
tbo frames aro at right angles to (.ho iixin. 
the micromotor screw gives tbo vnrmf u>iu in 
the length between tho two poml, 4 of 
])orl; on the test piece. To set (ho ft' 
normal t(> tho axis of the test bar, Im'i'ln 
aro attached to them. Level c on tin* J 
frame is adjusted by tho screw rf, wliiUi 
upper .frame is set love! by moaim * f 
micromotor screw c. The pressnro *n 
micrometer screw in thu.s 
constant, and equal to . I 

the weight of tlio upper 
frame. 
('17) (3jjrnr,B Mrono- 

METUIl tSciHJW (JOM1UNKIJ 

wi-nr A Jhrr,Tii'i,YiNu 

IJBVKR. (i.) Gamttt'$* 

Mxtenxameier, In this 

instrument (shown dia- 

grammatically in Fit/. 6Q) 

there is a mechanical 

magnification of two, combined with mini 

merit by mcaiiH of a single inicromotnt- JM* ..... 

Two pairs of steel plates 11 and am atf-tic >]i*>. I 

to tho test piece by screws 10, E and f >i vt r t << I 

together at V. The mioi-ometor M ia ]n\-,,l< , 

to the lower plates and carries a n|)im Mo M 

which passes through a guide K piv<>Lc*i] (., 

tho upper plates, Tho apimllo (iarrh-n n 

hardened pin on its upper end, nntl wli*>ii 

tbo test iiicco extends, tliis pin, wbieh fin j, in 

part of an aneroid haromotor, iimvcn, ( |,, f , 

aneroid noodle. Half of tho amount wlil'|4 

3 HRC i Johnson's Materials of Oonslrurtiait . J 1 1 | M 
11 lust. Civ. liny, ./'roc. c'x'xviii. 3^1.' , * *^* 



/ 



HI 




1 li 



">K 



-\i, . 



ELASTIC CONSTANTS 



I fit) 



Ihti micromotor has to bo moved to bring tins 
needle to its original position is a measure of 
tho extension. 

(ii.) Itichie hnproved extensome'ei; supplied 
by Messrs. Richie .Bros. Testing Machine Co., 
reads t.lio average stretch from two Hides of 
the test bar with one micromotor strew. The 
arrangement is shown diagrammaticaHy in 
Fly. 07. The two frames A and Ji' arc 
each fixed axially to tho tost piece by two 
hardened atcol - pointed thumb - screws S, S. 
Tho left-hand rod H is rigidly joined to the 
lower frame B and is pivoted to the upper 
one A. Tho right-hand rod swings from a 
pivot in tho upper frame over the micrometer 
screw in the lower one. The rods are equidis- 
tant from the points of attachment to the 
specimen, no that when elongation occurs the 
right-hand swinging rod moves away from tho 
micrometer twice the amount of the' elongation. 
This oxtensomoter can be used on gauge 
lengths from 2 in. upwards by having sets of 



__ Terminals for leads 
to ilrij cells 



Pluot- 



Top collar 

containing 

Insulating 

steuue 



This simple and accurate oxtonsomctor is 
made by tho Cambridge and Paul Instrument 
Go. Ltd., Cambridge, and is especially designed 
for use as a workshop instrument. It is eom- 





l<' III. 07. 

rods for those gauge lengths which are required. 
Elongations of 0-0001 in. can bo easily read, 
.and electric contacts can bo employed with 
the instrument. 

(iii.) The Cambridge ISxlenaomeler (J'Vjy, (SH). 



FIB. OH. 

posed of two separate frames, each of which is 
attached to the test bar M by hard steel conical 
points PP and P'l" arranged in geometric 
slides so that, after the points are gently 
driven into tho punch marks, they can bi> 
clamped in position by tho knurled bends 
II, .11. The lower frame curries a micro- 
meter screw It and a vertical arm IS at 
the top of which is n hardened steel knife 
edge about which the two fnunen work 
together. The micromotor mirew is pro- 
vided with a hardened steel point X over 
which a nickel-plated (lexil)le nlcel tongue 
A, forming a continuation of the upper 
frame, is carried. The tongue anil frame 
form a lever magnifying the extensions 
of the test piece by live. 

In use the vibration of the flexible 
tongue takes the place of the elcetrie 
contact, in the instruments previously 
described, as a delicate means of setting 
the micrometer screw. The steel (origue is 
vibrated and the screw tinned until the 
point X just touches the hardened knife 
edge of tho tongue ns it vibrates. .Head- 
ings can bo repeated by this means lo 
0-001 mm. under ordinary conditions of 
test. The standard instrument is suitable 
foi' specimens up to f in. diameter on a 
gauge length of ( or 2 in. 

(18) iNimiATimi .1)1 ATi ISffl'llUMKNTH.-- 
This typo of instrument eonsisls of one or 
more calibrated dials with pointers on nicely 
mounted spindles, These lake the place of 
the micromotor screws in the previous elans 
of oxtensometei's, and are self-indicaf.iii); 
for large or small deformations, They are 
generally used in eonjinmtron with some 
form of lever magnification. 
Messrs. T. Olson supply ft dial oxlonno- 
motor of exactly (ho samo form as nonning'n 
extensometer { (<lfi)) except that dials and 
sliding rods replace the micrometer screws, 
Tho sliding rods arc attached to the lower 



160 



ELASTIC CONSTANTS 



frame in plnne of the micrometer screws, ami 
spindles, carrying drums mid pointers, arc 
fixed to tho upper frame with their axes 
horizontal. These take; the place of tho pings 
f/. H ($' tf ,t- C'J-). The friction of the sliding rods 
against tho small drums ( I in. in circumference) 
cause Ihe latter to rotate. Thin also rotates 
tho spindles and pointers round calibrated 
discs. 

(4!)) 1)[AT, T'JXTBNSO.M KTEIIS WITH MECHANI- 
CAL MACLMl-'tOATIOJi. (i.) Uninilfiiitlf O/ Win- 

cons In WirciBOitud Jtlxtensamclcr. 1 This lias 
one dial attached to tho upper frame which 
in operated by a warn arranged to transmit 
twice the extension of the teat piece to the 
dial drum. 

(ii.) Ilurst-Toni1in.ion J'hic.n-mmeter (Com- 
bined Lever aiul Dial], Fiij. (if), This instru- 




inent has been especially designed fur use on 
the stundnrrl test piece- (0-5(14 in. diameter and 
2 in. gauge length) ; ib cnn ho used, however, on 
specimens up to one inch in diameter. The 
gauge length of 2 in. is not adjustable, but the 
instrument can hu attached to specimens of 
greater length than this if required, Jt is 
provided with two forked lovers, A and B, 
fitted at the fork with pointed clamping 
screws which, when tightened on. to the test 
piceu, form the- pivots of tho lovers, 

The dial indicator is attached to one end 
of tho upper lever, and tho other end, hoyond 
tho teat piece, has a stout vortical lug D ex- 
tending downwards from one extremity of tho 
forlc nearly to tho level of tho lower lever. 
Hero tho lug bends inwards, and one arm ]U 
of tho fork of tho lower lover extends inwards 
' ' tho samo way. 

Tim k\vn levers are connected by a short 

'on's ^fiitcriuls oj Construction, tills, 



length of piano wire which lies in tho central 
vertical plane of the two lovers. 

This forms an elastic hinge, HU that us tho 
test piece stretches tho free ends of the levers 
open away from one another. 

This method of comieetmg tho lovers also 
permits tho test piece to Mtraigliton out 
slightly under Iho load, if originally, slightly 
bent, without straining the oxtoiiNomcior. 

Tho lower lover is shorter t Imn Mm upper one, 
and it carries at tho free end a short vertical 
screw F with a largo milled heud. 

Tho end of the screw is rounded and polished, 
and boars on tho end of tho shorter arm of a 
third lever which is attached by a short 
length of flexible steel ribbon to a bracket 
which is screwed and dowelled to tho upper 
main lover. 

Tho end of tho longer arm of this third lover 
bears upwards on the end of tho plunger of tho 
dial indicator. 

The system of levers is proportioned so that 
tho movement transmitted to tho indicator is 
ten times the extension- of the teat piece. 

JJy turning tho milled head of the screw 1? 
tho dial indicator can bo brought to ucro before 
tho load is applied j a light spring maintains 
the end of the small lover in contact with the 
point of tho screw. While tho oxtentiomotor is 
being attached it is necessary for the two main 
levers to be rigidly locked, with tho axis of the 
clamping points parallel and at a distance of 
2 in, apart. 

This is accomplished by inserting two 
locking pins, one of which constrains tho axes 
to be panillol while tho other (ixes the distance 
between them. 

Tho first pin is placed in tho Htumi horizontal 
plane its tho wire hinge, and its axis intercepts 
tho centre of tho wire BO that tho insertion of 
this pin loaves the level's only OIKS degree of 
freedom. 

The second pin correctly fixes tho relative 
positions of the two lovers. 

In order to onsuro that tho clamping points 
shall grip tho test piece along a diamotor and 
not along a shorter chord, two msrtiwH are 
placed in tho forked part of each lever inclined 
at about 45, 

Tho axis of those screws intercept the axis 
of tho test pieco and the ends are roundod to 
bear at points on the tout piece. 

Tho usual diamotor of tho reduced part of 
tho tost piece is 0-504 in., which gives a cross- 
sectional area of 0-2fl s(|, in., and the length 
of the screws is such that when just tight the 
ends arc 0-282 in, away from tho vortical 
plane through the clamping points. 

When attaching tho extensometor it is 
simply hold up against tho test piece bearing 
on thoondsof thof on r screws, and Ihoolamping 
screws are tightened ami tho points pierce tho 
test piece- along two diameters. Tho extonso- 



ELASTIC CONSTANTS 



161 



meter is thus a self-contained marking-out jig. 
As soon as tho iiiHtriiment is fixed to tho lest 
piece tho four screws aro just slightly slackened 
so that they aro just clear while tho tost is 
being made. 

One division on the indicator corresponds 
to an extension of 0-flOOl in. and, by esti- 
mating,, tho extension csin bo readily measured 
to tlio nearest 0-OU002 in. This instrument 
is mado by Charles W. Cook, Ltd., Man- 
chest or. 

(iii.) JtifJih Dial ISxlensnmeter, A similar 
typo of dial oxtonsomoter is supplied by 
Messrs, Hiohlo Bros. Testing Machino Co. 
Tho instrument itself is not quite so elaborate, 





Uprifilit bolted 
[to frame of 
tliin Machine 



.if'io. 70. 

and requires n special mark ing -oil' block which 
i'orma part of tho on till;. 

(iv.) Jie.rry Ntrtn'n (linii/f. 1 (Combined Lever 
and T>tnl). Thia instrument measures tho 
deformation on tho surface of tho test bar or 
structure and in principle is a pair of beam 
oompiiHsos, one point of which is lixcd to tho 
frame- of tho instrument ami tho other operat- 
ing nil Amos Din! through a five to one bell- 
omnk lover. Tlio points of the instrument are 
placed in tho gaupo marks and an alteration 
in tho gauge length ia shown on tho Amen 
Dial. 

(fiO) M'lOllOHOm'I'l RlUIHNfJ EXTKNSO- 
Mimiiis. {(lA'riiUTnMKTmis.) With this typo 
oE instrument tlio diHlitnco between (inn 
scratches on tho test pioco is measured by 
sighting with a microscope on tho two scratches, 
and reading off tlio distance tho microseo])o han 
bcson moved along tho slide to which it is lixed. 

1 Jlinjiiit'crtng Jlct'ortl, Juuu II, 1DJO, 
vor, i 



Tho dotormination of elongations by this 
method in a lengthy process, and except for 
special purposes it has been abandoned. 

Fiij. 70 shown an arrangoinent of two micro- 
scopes which is convenient for measuring tho 
extensions of stranded cables. Microscope 
A has ordinary cross wires while microscope 
B is iittcd with a micro- 
motor eyepiece. Jioth in- 
struments are attached 
tt> a bar C which can ho 
moved vertically by the 
screw I). Both microscopes 
arc fooiisBcd on swatches 
on tho test piece and the 
load applied, By means 
of the HCI'CW 1) tho cross 
wire of tho top microscope 
A ia made to coincide again 




with tho top scratch, while 
tho adjustable cross wire 
is moved in tho second 
ji'Kt, 71, nnc.i'oseope to the now 

position of the bottom 
nmitdi. Tho movement of this cross wire in 
the calibrated micromotor eyepiece gives tho 
extension. 

8 (M) ClIMlUNlH) MlCHOHttOl'K AND LlJVKH 
.Hx'ri'iNKOAir.TUii. I'hviiitj Kxle.iinniiic.lcr," This 
instrument has beon used for a great deal 
of tho scientific work- in this country, It in 
shown diagrammatical!)' in Fin. 71, and in its 
latest form in Fly, 72. Tho two clips, li and 
0, are ouch attached to 
the tost picco A by two 
pointed screws. Clip Ji 
carries tho vortical pro- 
C jection B' (Fig. 71} tor- 
minuting in a rounded 
point 1', which engages 
with a conieal hole in 0. 
The pieces B and B' aro 
joined to one annthoi 1 in 
mioh a way that tho 
tost piece may twist a 
litllo with- 
out all'ccti- 
ing tho on- 
gagomont 
,of 1' with 

(J. When tho test piooo extends, I 1 serves an 
a fulcrum tor the clip 0, and point (J it! 
displaced through a distance oipiul to twieo 
the extension, This displacement !H measured 
by a microscope attached to B, sighting on. a 
mark on tho rod It hanging from tho point 
Q on tlio upper dip, Tho readings aro takun 
from a mioromotor sealo in tlio eyepiece of 

' Iton, too. I'nifi,, IHlMi, Ivlii. 12!l. 





102 



ELASTIC CONSTANTS 



tho mioniaciopo. The KUWW (lj, /-'/;/. 72) HOI-VCH 
lii) bring tho Higlifod nmrk to a con von lent 
point, on tho mienmielin 1 sci.'ilo and also 
determines |.hr acsalo readings which can lio 
Oiitinmted to (M)(W02 in. A oliunping bur is 
added l>y whioh (.lie r-lipH I! and aro held nt 
tlio (sormcit diNtamro whim fixing them on tlio 
tp.nd picfio, Tliis exl<iHHoniotB!' ia made by 
Mc.HSi'H. Tin; Cambridge & 1'mil Instrmnpiit 
Company I'm- gango lengths of '2 mid '8 in. and 
1.0 and 20 liwitirnotrca. 

An p;|)[)tii'atLis for marking off tlio gauge 




l-'ld. 72A. 



}H)ititM (/''(','/. V2A) 



with tho inatru- 



(\i 



jj (52)M.l)l J TII'r,YINO 

(i.) K(3nni!(ly l tltssigncd a Hiiii])lo lover (lever- 
np{() 100 to I) oxtiniBumotor oli|)])od to tho test. 
Imi 1 nt two ]iuinlH. 

Mai'tonn'n a lovor oxtoiiHinnolor is a mrnlifioii- 
l.ion of tho Konncdy inalnnnent, mill is 
ii-i'i'fLiifjisd t<i lnko HiniiiltanooiiK roadin^H mi 
twit o|jpimiLo sidcH uf tlio spiwinion. It ia 
i'M'iniabEc'tilly in Fig. 73, am! 
two cilijis 1J, .]> carrying tho 
(', (J, and hold on pnoaito 
mdtia uf Mm H|iu(simon iiy n, spring R, Diainond- 
HliujHid pieni'.i A, A, t wliich tho arms .1!, B 
Jim al-tiusliixl, am pivotoil in shallow 
fnnniul in Mii> i)li[)H 1), 1). AVitli a 
(ion of lifly, readings HIM easily bo niado to 
()-(2 mm. ' 

(ii.) AViHHfirff/.v a horizontal euteiifwinfitf.r \a 
j, r ri|>|!(l im liho hai 1 at four points in an axial 
jiluno and enimiHlii of two frainoa, ono lixial to 
onisli j;iui)fo initrk, whiuli real on oaiili othor 
ovor tint poliiLn o{ atlimhinonfc to tlio last har. 
A li^ht poiuti!!' in prnvided with two stool 
pDinU, DUO resting mi ouch frame. When tlio 
LisHt Iwif oloiif^atus tho two points inovo 
rclutivoly tu otioli othnr in an axial dirootion, 
mid tliin nutvoinont i innffnificd by tlio ond 
of fclui ptmttor which trnvols ovor n sonlo 
oarriod by a rod attached to ono of the 
f ran ION. 

Otlmr iiiiilnmHiiilfi of this typo havo boon 
by iSlronusyei 1 ,' 1 Goodiiuui) 5 Wiok- 



1 Fust. I'ir. Kna. /'cor. Isxlv., nlflo Ixxxvlli. 24. 
" HunillHHtk ! 'i'l'Kliau, I. r..in. 
a f'liniini'i'rlni/, Wi!|i(.. t'2, IHillK 

* I nut. AVjiW jlrrtiitirts, Truitx., IH8H, i>. ;)S, "A 
Ulraln linlli'iidn- rut 1 I'm; nt Him." 

* tinyitKcritiy, HupL Li, EHUD, 



st(!fid, n AKlicroft,' Ool. W. II. J.'aiiK' 
JJupny." 

(fffi) Ol'TfCJAL MAflNIFVINO ExTKNHO j" 

For gi-oator nocunioy than 0-00002 
nionsiiring deformations some form of 
lovor ia generally employed in \vli* ! 
cliango of length (if tho Lost piece in <:i>ri 
into rotary motion of a mirror wliich in ci 
by means of a telescope and atsalo. 
oxtoiiHoniotoi'.i emjiloy two inirroi'.s in 
roadingH arc obtained from oppoHito 
tho test liar, while in others tlio moan ox 



i"- 
>r*' 
' 1 



r&st Piece 




via, vs. 

is measured by tho reading from a 
mirror, 

(i.) Two Mirror Apparatitft. Baunc./i-i n*t* *' !t 
Instrument. 10 Tho introdnotion of nih'i r < *r t*\- 
toiiBoinotors is ]irineipally duo to BuuHdli iit^cr, 
who designed tho instrument shown in f^iff, 71, 

8 lust, Mee.h. ling. I'rof.., 1004, p. -185. 

7 Discussion on Unwiii'a pupcr on " *rt,nt'^|p 
'Pests on Mild 8tol," Iiixt. (Jlf. Kttff. 1'rua. xiv 
2(10. 

8 Mnrtens's IlandtiooJt of Testing, ]>. 545. 

8 Aniwles ties Pouts ct (Jhaitssi'es, 5tli Horli.>H. ^ilv 
381. 

10 Maschiite zmii J'rilfen cler J-'t-flitfA-f ft ,/, r 
Matfriatirn construirt row Lwlwig ~\\'r,rtfar, nmt 
liiftfitmente znm Messen dm Gestttllm'erdflitprttriff t f, r 
J'rnliekiirper, eonstntirt von Jon, Jtauschinger, iM tl tmfu-n 



ELASTIC CONSTANTS 



103 



Two clips, <t, a and b, b, am pressed against 
tlio specimen : e, c, are light springs which 
press outwards aguinst the rollers d, (/. Those 
rollers, which uro o caoutchouc, aro carried 




FIG. 74. 



by tho oli]> b, b, and themselves carry the 
mirrors 17, g, AH the specimen extends the 
rollers rotate, and these rotations iirc measured 
hy mcaiia of Iho telescopes K, E and scales 
/, /. The results aro recorded to 0-0001 mm. 

(ii.) Martcntfti Mirror Exlcnsomf.tcr. Tliis ia 
an improvement of BaiiBohiiigor's instrument 
and is shown in fig, 75. It is cxtromoly 
aoourato and sensitive and is most adaptable. 
In this arrangement the multiplying levers of 
Murtcns's lover extensometcr (Fig. 73) nro 
roj)lnt)cd by small mirrors (tn, in, Fig. 75) 
which aro afctaclicd to the rhombic-shaped 
])iccBS of steel acting as fulcra, in sueh a way 
that the- reflecting surface of each inirmr is 
on the axia of the fulcrum. The two clips 
d, d aro hold on opposite sides of the specimen 
hy a spring .1 which rests in grooves c, c. 
lOaoli clip is pointed at one end which IH gripped 
directly on the tost bar, while the other end 
IULH the rhombic piece intorposcd between it 
and the bar. The mirror is mounted in a 
frame by moans of pivots centred in small 



holes drilled in the glass. In order to adjust 
the position of the mirror the frame is free 




to revolve on the axis of the rhomb. An 
adjusting screw Ii and spring p aro placed 
on opposite sides of tho mirror to control its 





S/ite Eltvaiian 
rt cmiilttfj 



Scale 
! j 3 4 g fr_7_$ ? join 



Fin. 70. 



ELASTIC CONSTANTS 



position about an axis at right angles to that 
of the rhoinh. 

A pointer Q is attached to the rhomb and 
arranged so (.hat, when it coincides with a 



Cross Wlro 




Slit for lief lection 
from Right Hanil Mirror 



Slit for Reflection 
from left Hand Mirror 



mark on tin* dip ,} t I,),,, instrument IH Hot at 
tilt! propor gaugo length. 

Extension of the lest pieeu rotates tlio 
rJmmliN, and tlio angular rotation ia measured 
by a scfilo and telescopes us described for 
Jiaiisehiu^or'B oxtoiiHoniotor. Two readings 
aro nociwHiuy, ono for each rhomb, and two 
telescopes aro usually employed. 

At tlio .N.I.YU a " ono telescope " arrange- 
ment has been in use for sonio yours with 
complete sneoess. This ia shown diagram- 
matically in Fig. 70. 

Tlio tolcscopo T is nttachcd to a support 
S. Immediately iimlor tlio telescope, and 
attached to tlio same support, is a platform 
P whoso height from the grmind can be 
quioldy Adjusted. It can bo 
locked in any position by , 
knurled -headed KOIDW A, Tlio 
telescope firniiiffcmciit is kept 
in contact with the platform by 
means of a Hpring B, and their 
relative position in a liori^ontjil 
piano enn lie accurately adjusted by means of 
the |)ivnt(!(l nut and screw 0. 

The platform (Mimes an illuminated scale 
B, two fixed mirrors J[j and M a) and two 
iniiTom "N a utul lY, pivotod vorticolly HO thai) 
their position can bo altered by means of tlio 
aci'ow and spring K 

The illuminated Hcalo ia ro- 
fleotctl from ono of tlio " Afnrtoiifl " 
rotating nrirrora on to the pivoted 
mirror N,, and tlio angle of this 
is adjusted to bring the reflec- 
tion into tlio telescope by means 
of the fixed mirror M t . The 
other "Martens" mirror is imulo to reflect 
tho illiiniinalod scale on to the pivoted 
mirror N 2 , and this is adjusted to bring the 
reflection into tho same telescope. The 
flifforoiKm Jxjlwouii the lengtliH of the two rays 
is no small thai the telescope oan, at the sumo 
time, focus tho scales reflected by each of tho 
Martens rotating mirniro. Tho mirrors reflect 
" ghosts,' 1 mid these are out out by inserting 



I.I 



a mask (7<Vr/. 77) in tho cyepi <ui 
tolesc(>j)e, and by having adjus|.ii1*1f* 
sliatles (.R, Fir/. 7fi) fi.ved m l )( ,..t'.c' 
mirrors on tho platform and the oxtniiH** 1111 '* 1 '' 
The mirrors used must be absolutely ' Jl ' 1 
and gi'cat earo should be taken to H*"*' ''J'" 
they are not distorleil \vbon they arc *sl" '" \ n ' 
in powition. 

A eurvod scale should lie used, but !<?*** liii).; 
eun bo taken on a straight sealo ^*i ( l i 
eorrootion applied. The iliuim'nal.i^l i 
graduated in millimetres and readings 
suiilo can lie estimated fo O'l mm, 
Tf /= tho wiilth of tho rhombs, 

L= distance fi'om the sealo to tho 

the tc^t piece, 

* extension of tho te.st piece, 
X^Btiin of tho readings from tJ 
Martens mirrors. 



Usual values of / and L aro 0-180 in. 



t in 
(he 





Plan 



. 7ft. 



45-0 in. respectively. If X ia moasuiroil in 
millimetres wo have 



By providing snitablo elirm this oxtouo- 



ELASTIC CONSTANTS 



meter can bo used mi gauge lengths fmm ono 
inch iipwanh jmd with tost piowy from (MW 
to 0-8 in. diameter. 

An instrument using Alartciin'ti method but 
of slightly different design In thut shown in 
J'Vf/. 7(i iii HiippJiod by JleaHi-fl. Alfred J. Amsloi- 
& Co., iSohan'hiiiiscsn. 

(iii.) Westiurjhnutm Wire Vctling Kxfensonicler, 
This instrument, dosignud by LyiKih&lirace 1 
for extonsoniotor lusts on small sections such 
as wire, ribbon, etc., ia shown in J'V</. 78. It 
consists of two clips A t and A,,, fastened at 
one cud to a slotted block E, while tlio free 





l-'ia, 70. 



ends carry hardened rollers, Cj and C 3 , which 
can turn in pivot bearings. 

One end of tho instrument is clumped to 
tho tost piece Iictwecn tho spring G and the- 
block J!, mid tlici rollora 0, and O a arc sprung 
(i]iarfc to take the test piece at tho other ontl. 
Piano mirrors arc uttaulied to tlio rollers, 
which arc arranged so that a spot of light 
from a lamp D is reflected from tho mirror 
Cj to miiror C 2 , and thoneo to tho curved 



With this oxtensometcr increases of length 
of 0-00002 in, can bo monaural. 

(iv.) Singh Mirror Apparatus, Nurmiv's Hx- 
lensamcler,' 3 This instrument is a combination 
of Swing's lovor arrangoniont for making tho 
oxtonsomctcr indiaito tho menu st.r.ain, with 
a iniiTor method of measuring that strain. 

1 " Wiro 'LVsfciuw lixleiiHomnlfii 1 ," J'roa, Amer. fSw. 
Test. Mat., 1010, xlx. narfc Ji, p. MO, 
B Jnsl. Mech. Ki\g. Pros., JliOJ, JI. 400. 



.1 05 



9. 



T 



It is .shown (liiigmmmaUcHlly 
The attach in on i to tho tsfc p 
four sot B(!i p (*\vs A A and .HH. A A KITWH 
as a fiileruni Ii' t!io top unniilfir ring (.', mid 
when tho tout jiioco oxLunds, Hie muvorin'iiit 
botwecn and I' 1 (\\ r bicli i an oxtaii-sion "f 
tho boltdiH ring i)) i.s iip[>nixmiiili)ly L\viro 
tho extension. >So fur tlin pnin'i])lo i tho 
sumo iia that of ttii! Irving oxttKisojimlt 1 :!', 
but wfiei'oaa Jiving inoamn-ca this oxt<iiiHi<>ii 
by a niici-oinoltn 1 inicroH^opp, Jlornnv IIHC:H H, 
" MartoiiH *' I'liumb .11 to which a mirror .N 
is attached in 11 vertical position. 

A second mirror SI in pcrainn<mtly fixed 
to I' 1 . Tho iningcs uf llus sisulo from l>i>Mi 
iiiirrora aro seen oitlo ly fsiiio in tho toUwop!). 
An inclox mark iy takoii on the iniHgo of o\l 
for reading tho niovoinont uf N. J5y thin 
menus allowance i.s mado for nny move-intuit' 
of tho teat JHIJISO and oxtoiiHnmoUsr, us a wluths, 
relative to the position of tho tcl<!Hun[)o. 

Witli tho iiiHtrumrait aa lined by Morrow M u> 
oxtonsion of tho spcciinon is ohtainod It). th 
ncarofit v:iii(i..iiro of n iiH'h. 

Uthoi- singlo miiToi- oxtonstimotors IHLVO 



uml 




liy Uiu\-i)i, n 



illHll'U- 



een i(wg 
ILartiy/ 1 

jj (fi4) OoMI'liUHHO-MK 

rnonts nsod for ton.iilo nxpni'iitKintt) onn nlmt 
ho iiHisd an ooinpnjHsomofcdi'H jirovidoil lliul. 
thu tent |)iiH;o !H of Hidlidtmt length io Inlvn 
tho.ni. It is, liowovor, often ncctNHary t" 
modify tho mothud of aKatil uncut. '.I 'Iin 
conditions applioablo to tins HMO of oxlriiHn- 
JtiotorH ( (^llt)) apply, with just us uuioh fm-irr, 
to c,'oinj)rcHSonn>t()rri. 

The Ytilo ox-tonsometor ( ('tfy), UHitig donhlo 
inierometei 1 scrowH, mid Mm Wisconsin (|) (-(II-)) 
dial exlcnsnincler ar both used in tho U.S.A. 
for (lonipi'tiBsion tests by a Hiiitablo i modi(uiiiti< m 
of tlio clanqiH, 

.Kwing'a comjirosaomfitei 1 fur shoii lilnrku 
(Pig. SO) in on the tuimu 
used for toiiHioJi testa. 
multiplication in, however, 
limes, enabling roudings of i 
to ho obtained. 

Marlcns'n mirror at'Timgomofit (Jf'ifj. 
Ijcon usod by tho tuithor JIH a 
nicter on tliamotora iip to '\& in. by 
additional BprhiyH S to hold tho ulipa on 
tho larger fliao of test piece, 

Unwin has doaignud an iiiHlnuniml fur 
fihort blocks combining lovor and 



n.i ilinL. 



i 
f an 



8 J'Ays. Not. i*n>c., 1880, vill, 178. 

1 Ilatullttwk nf T(:stifi t imvl 1. p. GOU. 

1 Uisilingf.meur, 18US, piirb vj, 

' Testing Materials of (Jomtruclian, 1910, p. ilill. 



166 



ELASTIC CONSTANTS 



This instrument is shown dingrammatically 
in ./'';'(/. 81. Tho lever L,, having a knife 
edge resting on tho pillar 1', gives a mechanical 
magnification of 2,1, The frame \ 1 . 1 in fixed 
to tlic .specimen by four screws, and both 
frame I/, and lover L t carry silver plafes 
on their ends having a fine scratch on each. 
The distance between these scratches is 



.tilierometD, 



Testing Mae hi no 
/ Platan 



Silver Plates cadi engraved 
with a fine scratali 




tfio vernier and for any change of length 
specimen during test. 

(ii.) Cuke.r's To>-f/ nonet KI: Z Tho tot' 
strain is measured by this indicator 
length of 8 in. At one end of tho 
men a graduated circular pinto is ni<t 
to tho gauge mark by three set B< 
This plate carries an arm and "\ T 
which em 
moved rmii 
and to wli 
attached a 
carrying a 
wire and mi 
At tho < 
gauge mm 
cliiiclt, also 
by throo 
screws, HU;| 
an arm ha-v 
micromotor 



measured by tho mioromotor microscope i\r. 
Alterations of this distance with load (five 
tho compresaivo strain as Iho moan of that on 
tho two Hides of Iho block. 

(fifi) TOKSIONAT, STRAIN INIUOA.TOHS. i'or 
measuring clastic deformations in torsion, in 
order to determine llio coefficient of rigidity, 
accurate obsorvationa arc necessary. All 
instruments for this purpose should bo 
independently fixed on the bar with a definite 
gauge length. 

Where a high degree of aeouraoy is not 
essential, a convenient and simple method is 
to damp two long pointers on to tho specimen 



on to tho cross wiro of tlio vei-niec 
frame. 

When the torque IH ap|iliod to the teat 
tho cross wire moves relatively to tho n 
scope, and tho amount of this movoim 
measured by tho mioroinotor eyopioe 
about one second of are. When tho i 
lias exceeded, tho range of tho oyo])i(! 
cross \viro can bo readjusted to xero by in 
cho ci'osH-wiro arm round tho oirenlar pin 
means of a langont screw. 

(iii.) Unwin's Torsion Mie,roiclar. s -~ 
instrument fusts on tlio siuno prinniplo u* 
designed by Cokor. Thcro arc, howevoi 




\ 

at a given distance apart and obacrvo 
their movement over a fixed scale. Tho 
dilYoronco between the readings is a' 
measure of tho toraional strain, 

(i.) Porter's Torsion Indicator. 1 In this 
indicator tho long pointers of tho above 
instrument are .replaced by two rings clamped 
to tho test piece at a gauge length of 3 in. by 
three sot serows. One clamped ring is 
graduated in degrees and carries on it a 
concentric ring engraved with a vernier 
reading to five seconds of angle. Tho vernier 
ring if! mipporlnd on ball bearings and ia 
operated by an arm fixed to tho second 
olamped ring, i'roviwion is made for sotting 

1 Amer. Hoc, %'csl. Mat, x. 578, 



Via. 82. 



or two slight differences in detail, 
Unwin's method tho microscope, utfci 
to a projection from one clip, sights on 
finely divided scale on tho other cli| 
gauge length of 6 in. Tho mieromoto-i- 
piece reads to O'OOO degree. 

(iv.) Mirror TorquMnctar, The motho* 
ployed at tho N.P.L.' 1 is shown in Wig, HU 
consists of two small clips, A : and A a , 

1 Hoy. Soc. Edinburgh Trans, xl. purt II. ]>. ^(1! 
3 't't-stiiiy Materials of Construction, 1010, n-. 
* Hatsoii, lust, Ateeh, Jlng. I'ruo,, March 
1>. 183, ; 



ELASTIC CONSTANTS 



107 



fastened to tlio test \nw.o by three pointed set 
screws C. Attaclicd lo tlieae clips auo the 
adjustable mirrors 15, and Ii 2 of a Martens 
iniiTor extonsoinotoi 1 . Tho mirrors are 
arranged, on a gauge length of four 111(11)0.1, so 
that they arc in tlic vertical plane passing 



neutral axis of Uio bourn, Thin 




is not fulfilled by Hit) IDVOV 

(2) The mean deflection should IKS ubtiuiuid. 
Tlio ammralus should cither provide for tultin^ 
readings on both sides of the fi'.st pic-eo or 
automatically givo the mean deflection. Thin 



Machine Head 





\ 1 / Pin on 
yf/ of Tost 


Neutral Axis 
Piece 








i. 


"^Vn 


A . 




N x T ~T ._ 




through tho a-xis of tlio test piece. The 
method of measuring tlio movement of Iho 
two mirrors by Iho use of a single telescope 
has already been dustsribed ( (03)). Tlio 
difference between tlio readings from eneb 
iiiimii 1 at small inurements of Liu; lonjuo givo, 
when multiplied by n constant depending on 
tlio scale fiistaiieo, tlio angle of twist 
for that increment on n length of four 
iuclies. 

(60) DEFLBOTOMErEnH. TIlOSO ill- 
Htrunients arc used t{> jneaaiiro tho 
amount of bending of beams, ote., dur- 
ing a. trans voreo tost. 

Commercially a multiplying lover 
(lortflctoinetor (Fig. 00) is generally 
employed or a strainod-wiro arrango- 
nioiit may bo uaed where largo deflec- 
tions are to lie measured. Tills is 
shown in Fig. 83. A lino wire W is 
Btraincd between two pins fixed on the 
neutral axis of the beam above tlio 
supports and kept taut by a rubber 
"band It. This forms a datum line. A 
polished scale S is graduated cither 
in mm. or inches and suspended from 
tho neutral axis at the centre of tho 
beam. The observer brings hia eye to snob 
a position that tho wire and its imago in tho 
polished scale coincide, and ho then reads tlio 
position of tho wire on the scale. 

For most work an nccurnoy of 0001 in. is 
usually sufficient. 

Tho methods described above do not fulfil 
some of tlie essential conditions for accuracy, 



condition in not tiocomplishud by the stmined- 
wii'o arrangement. 

(i")7) Al'l'AKATUS roil MI'MHUHINO LATKIUh 

STHAINH. (i.) <.!ok(.r'a Lateral 8tr(iin-iiif.<tmtriu(i 
Apparatus. 1 Tliia itiHlnmiitiil in shown iliu- 
grammatically in Fly. 8<l and eonniNlH of two 
lubiilai' arms A, and A a comiculnd by a 




(!) Tho apparatus should ho designed to 
give tho relative deflections of points in tho 



Fid. 81. 



flexible steel plato li wliich forma tho f nluruiu. 
Tho steel plate is gripped by two collars C(! t 
one of wliich onrric3 nn adjustable stsrow '\i, 
which hears on tiio tost pieco and heops Ihn 
instnunont from turning. Tho arms aro 
attached to tho test piece T by two sorowfl 
D.D, tlio pressure on wliioh is provided, by tho 
compression of a spiral spring S oil tllO 
opposite side of the fulcrum. 
Tho iirm A a has a projection H , tlui end 
1 Hoy. Soe, Edinburoh Trans, xxv. part 1, p. 452. 



1(18 



ELASTIC CONSTANTS 



of wliioli id opposite io tho arm A ( awl if, 
arranged lo spring Inwards it, gripping a 
huifn i-<!^(i ,)'. 

Any (ihnngci in llic diameter of the test 
piece W1HS03 a cohitivo movement between tho 
one] oif f.ho nn A l imd tho prnj ration 11 of 
tlio ni'iti An, Tins movement rotali-s the itnifo 
edge .1, ia which u mirror K is attached. 
Tim rolalimi of |,lii.4 mirror is observed by a 
lel('seo[ji! and scale and ives n rmmsnro of tho 
allural.ion in tho diameter of the tost piece. 




I'Mll. Sli. 

Tlio Hcalo <lin1,iiii(!o EH arranged HO Umfc eaeh 
Kciilo division rojmtsenlfi O-OOUOOl in. 

(Ji.) J\ftifn>Hf\ l > hifttnuiiGnt for mmstn-ing Uic 
Lali-rtil CnietritcMon of Tie Jiurs. Thin instru- 
ment, 1 Hlicnvn dm^ramniiiticidly in Fig. 8/5, 
U!HD nst'H 4p|.iwil means of inensuniig ilio 
rdiiUvo (lisplaudiiioat ()P two arms. 

Two uriiia KK and LL arc pivoted at F 
4unl two fwsi'cwH A and !li grip the teat piece T 
and ni'o prc?Nsod inwards hy tilt sjirings 0. 
A Halation in tlio iliiuiiotor of the test piece 
onuses arm 1C to fall rolutivoly to t!io arm L. 
This roliitlvu motion is meiimired by tlio tilt 



r i hi- 

, f.liin 



' '"' 



of obtaining the constants of cxlcnHOti'"-' 1 

(1} By mca,siirenn;]it of the Icvon i " t? * ' 
instrument. In sumo types of a.pp EL rti t- "*-" 
can bo carried out BiLcacssfully, \V'H-l< 
Marions mirror cxtensomettsr tlio e 
depends on tbo width of the rhombs ii.ii*' 
scale distance. The former can bo delo!"* 11 iitrd 
by an iioourato meannnng machines Jin*' ^ 
latter \a usually adjiiHtcd by seltinjr' ilio Ht'-ril' 1 
distiinco from the test pieces |>y inoiUJ 6 * <J ^ ll 
gauge of known length. 

(2) Hy teat on a steel test ]>it-no ^vli"'"" 
elastic constanls have been aconratelv el*'**"'* 
mined. The tost piece is gripped. " in 1-Jn 
testing nmuhino in such a \vay that tlit* wlrT'ni-H.H 
is diHtributed in tho proper inaniioi' **it'l 
reading of the [V]>[iai'atii8 whieli is i: * ' '" 
calibrated taken at definite incrcnieniH *'f '^ ll * 
load. Thcsie readings are then compare I 
those calculated from tho known claH(.i<' 
HtantH. JE possible, a Hlaiulardisod appiLi-iit-ii'* in 
attached to the tost pieeo at tho HIIIIK' tiitio 
us tho ono whose c:ons(aiitg are riiiknci\vii tmt[ 
& direct eompai'iKoii made. 

(\i) Hy a calibrating insti'iniiont. An iiHC-rii- 
ment used by tho author is shown in ./'"if/. HU 
and consists of a stand D aurryii i|-5 I-AVU 
arms Hj and K a . Theao arms are tn * jvatlln 
along n feathor on the stand so that i-hi-ir 
position can ho adjusted. They am 1 u irc<l 
accurately in lino to take two rods A ti-iicl !H. 




lit a mirror M wliich is BLipporlnd on throe 
points, two of ivhiuh rest on arm L and ono 
(m ami K, A vortical mirror, not shown, 
isi also fixed to L at the aide of tho tilting 
mirror H and serves a.s an index for that 
mirror, iliu.s eliminating any errors duo to tho 
iiiHlnnmml moving relatively to (.he observing 
(.ulo.Hiiopo. The instruiiient is halanecd by a 
woijjht \V. 

/ JAlilHHATION OK 

Arj'AliA'l'UH.- Th 

IIW, 1'hil. Mat/., lOUl 






usual methods 
, vl. -JLV. 



U id iixed, hut A can bo movetl up 
and down by a micromotor head O?. A 

also works along a feather which j>JL p ov.*n(-!i 
rotation. 

The apparatus to Lc calibrated is attfttntn-d 
to A and I! and ita readings compar.tri'1 \vilti 
the movement of tho micrometer head. 'flio 
pitch of tho micromotor screw iw 0-O2f> jn. 
and the head if) divided into 2.1 purls mi t,lif^|, 
one division of tho head (aboiif; in.. ltnn) 
corresponds to (i movoinonfc of 0-001 in, 

it is essential that tho desired r<;it<.]iiitr 



ELASTIC CONSTANTS 



100 



should always lie approached in the fame direc- 
tion in order to eliminate) any backlash in 
tho screw. As tlio accuracy of tho calibration 
depends upon tlio accuracy of iho screw, this 
has been determined on a screw-measuring 
machine and a correction curve obtained 
for it. 

(.19) AuTOOiiAi'inc R-KtJOKniNti AITAHATUS. 
Tho deformation co-ordinate of the curve is 
always recorded directly from the- test piece 
ilaulf , usually with some form of multiplication. 
Tim main difference in the various types of 
recorders is in tho method of obtaining tho 
load co-ordinate. Thero are two principal ways 
in wlii eli this is done : 

(i.) Load recorded by tho movement of the 
counterpoise with or without automatic 
adjustment. 

(ii.) Load co - ordinato obtained by tho 
deformation of a calibrated spring. 

Tho early diagramming apparatuses wore 
applied to pendulum machines. Thurston, in 
187(i, designed the torsion test apparatus 
described in (10), and, in 1877, Abbott con- 
structed a recorder adapted to a machine in 
which the pull from a hydraulic press is 
transmitted through the test piece to a pen- 
dulum, the angular rise of which gives a 
measure of the load, An improved apparatus 
of the Maine kind was used by I'ohlmeyei' in 
1882, and more recently by tho N.P.L. for 
tests of copper and lmm/,o wires fully described 
in the British Engineering Standards Asso- 
ciation Report, No. 55. 

((50) AUTOGUAl'IIIO Al'J'AHATUS, KKCOKD- 

INO POSITION 01- COUSTEUI'OIBK. In 
machines having a moving counterpoise tho 
load co-oi'dinato is obtained from tho posi- 
tion of tho counterpoise on tho beam by 
moving a drum or pencil, by suitable pulleys 
or gearing, from tho shaft or screw winch 
drives the counterpoise. The beam ia usually 
kept floating by moving tho poise by hand 
adjustment. By this means, however, tho 
reduction of load at tho yield point cannot bo 
obtained and the final reduction, when the 
test piece is stretching locally, is only imper- 
fectly rep rod 11 cod . 

JlieMe Autographic and Automatic. Ay- 
parulus, In somo American machines an 
iiutograpliio apparatus is provided having an 
automatic weighing device. This device is 
designed to move the poise on the beam auto- 
matically to balance the load on tho specimen. 
In the Richie machine the scale beam on 
rising or falling completes an electric circuit 
at tho top or bottom stop in tho beam stand. 
Each circuit ia separate and connected to a 
magnet. 

Tho driving pulley of the machine turns a 
horizontal shaft which has a cast-iron disc 
on its end. This disc in turn drives one of 
two fibre wheels located equidistant on either 



skio <if the centre of the disc, 'Much fibre 
wheel has an armature controlled by one of 
tho magnets of tho electric circuits mentioned 
above. Thus when tho beam rises and com- 
plclcs the top circuit, one of the magnets 
attracts its armature, causing one of tho fibre 
wheels to engage with the cast-iron disc and 
drivo the poise alnny the beam anil so balance 
the load. When the beam drops and bits the 
lower contact, the armature of the other Jibi'o 
wheel is attracted by its magnet, which brings 
this fibre wheel on to the cast-iron dJHc and 
drives tho poise in the opposite direction. 

Tho screw which drives tlic poise also, 
through gearing, drives the recording pencil 
axially along the drum, HO that the reading 
of tho load, wluch is recorded, corresponds 
directly to the load weighed. 

The other ordiimlo is obtained by the drum 
revolving proportionally to the deformation, 
" Fingers " rest on top of U clamps fastened 
to the specimen by hardened steel- pointed set 
screws at the correct gauge distance. Tho 
lower " finger " moves downwards as tho test 
piece extends and by means of a rack and 
pinion converts this motion into a rotary one 
revolving the drum through mitre wheels. 
Tho actual extension is magnified five times. 
The fingers are HO arranged with clamps on 
telescopic tubing Unit only the exl minion 
between the U clamps is recorded on the 
diagram. 

((')!) AUTUCHAI'ITKI Al'I'AUATIIH 1IHINII A 

CAUIIHATKO Hi'uiNd. (i.) Thin method is used 
in two Wiokstcod recorders. In the curlier 
apparatus l tho measurement of the stress is 
entirely independent of the position of the poise 
on the beam, but is taken us being proportional 
to the compression of a helical spring acted upon 
by an auxiliary plunger operated by hydraulic 
pressure from tho straining cylinder of tho 
testing machine. As the load is applied by the 
straining cylinder it is balanced by running 
the poise along the beam, and the hydraulic 
pressure in both tho straining cylinder mid 
the auxiliary cylinder increases. The auxiliary 
plunger therefore compresses the spring, and 
tho amount of the movement of the spring is 
recorded by a pencil on the recording paper 
in a direction parallel to the axis of the drum, 
The drum is also given a rotation propor- 
tional to the extension of tho test piece and 
an automatic diagram is thus drawn. 

Tho auxiliary plunger is rotated during tho 
test in order to eliminate the friction as far as 
possible. The yield and maximum loads arc 
noted from the position of the counterpoise, 
in order to fix tho loud scale of the diagram. 

(ii.) 'J'ltB Bucl-loii Wic.ksle&l Patent Spring 
Balanced Recorder is entirely automatic, tin) 
variations in tho resistance of tho specimen 
are accurately recorded, Tlic action of 

1 Wlckstccd, Itisl, Mccli, Kng. Pros., 1880, p, 27. 



170 



ELASTIC CONSTANTS 



the recorder is shown iliagiumnmtieally in 
Fig. H7. Tlio counterpoise \V is placed 
nt tlic end of its travel, thus extending tin; 
spring S. AH the loud W is applied to 
the teat piece an equivalent loud is released 
from the spring 8, which therefore contracts. 
The amount of this reduction in length 
is proportional to the load on the lost piece 
and is registered on tin; recording drum It 
by means of a cord C passing over fixed 
pulleys 1'] and P 3 find attadicd l.o the 
pencil .1) of the apparatus. 

The load in Hum recorded axially, nnd (ho 



in xcrics with a stronger bar '.!(,' (tailed a 
spring-piece, and the two, which are eonneeted 
directly by a simple coupling, arc pulled 
simultaneously, the one through the other. 
The spring-piece is of u material such that its 
limit of elasticity occurs only at a loud greater 
than that which will break tin! test piece. It 
iniiHt also be of 
material asoer- 
~^ tained by previous 
Jt experiment to be 
perfectly elastic, 
so that its exten- 



rum ia rotated by tlic movement of tho lower 


ntaclietlto 5 
''<"< (T) ^ 


5 sion in strictly 
S proportional to 
3 tlio pull on it, and 
ib therefore to the 
pull on the lest- 
g? bar. .By a wimple 
arrangement a 
very light pointer 


Attached to lieam- 
Sttpport 

Testing Machlna Beam 




P. 


f 


1 




^ fo\ /p\ 


C 




Chain tulijeh'^^ [[g 


? f! 


f 

C 


c c 

-^ .^ 


i 

FlO. 


( 
87, 




T 


S' c is made to 
awing about an 
axis through an 
angle proportion- 
ate to the oxten- 
r> ^ Hion of the spring, 
piece, and propor- 
tional therefore to 
tlio pull on the 
test-bar. Tlio find 
of this pointer in 
its motion always 
touches a sheet 


W 




,'l 


L 


_l) 

x 



pulling licad relatively to thai; of the upper 
shackle, to givo the deformation co-firdiiinlo. 
AH the defin-mation ia not communicated from 
a fixed gauge length of the teat piece, it includes 
movement in tho grips and cannot be taken 
as tho extension of lljo specimen, 

(iii.) Moore's A utoyntphic .Ilecorder ' ia very 
similar in action to the Wibksted spring ro- 
eordor just diisoriljcd, the only difference lieing 
that the spring ta placed on tlio othor side of 
tho principal knife edge MO (hat when tho poiao 
i run out the spring in compressed. AH tho 
load is applied to Uio specimen UTI equivalent 
load ia released from the spring, which elon- 
gates until equilibrium ia established, Mooro 
used a steam-engine indicator ; iho spring of 
the indicator is attached to the beam of tlio 
testing machine to give tho load co-ordinato, 
and tho cord of tho indicator is attached to 
the test piece to record tho extension, 

(iv.) Kennedy- Ashnrojt ttccorthr fl (Fiff. 88), 
Full details of this recorder aro given in 
Kennedy's paper to tho Institution of Civil 
1'jiigtMt'uj's, and tho following description of tho 
principle of the apparatus is also taken from 
that paper : 
" The lest pieeo ' a ' in placed in tho machine 

1 Vroe. Amer. fine. Vest. Ma!., 30U8, vill, 053. 
1 /ns(. Civ, Jing, Proa., 1880-87, p, 31. 



of smoked glass ' rf, 1 to ivhieh in given a 
travel in its own plane proportional to the 
extension of tho test piece, and in this way 
tho diagram is drawn. Jiy an arrangement 
of differential levers it is assured that the 
motion of tho glass depends solely on the 
extension between the marked points on the 
test-bar, so that no amount of extension of 
the coupling, in the ends of the test piceo, or 
in any other part of Hie apparatus, can move 
tho glass. The apparatus is also HO arranged 
that tho absolute elongation of the Hpring- 




, 88. 



piece does not cause any motion of tho pointer 
relatively to tho glass." 

(v.) Ditlbi/'s Oplknl liwor<hi: n 'VMti ap- 
paratus is Hhown dingrammatieally in /''i>/. HO. 
It is similar to the Konnody-Anlmrnft recorder 
in that tho load is obtained from tlio extensions 
of a bar noting as a very stiff spring, Imt 
wlierena Kennedy uses mechanical menus of 
increasing and transferring these extensions 

3 lion. Sac. Pro?.., Mil!". Ixxxvl.A, and JUKI, 
JxxxvJii.A. ' 



ELASTIC CONSTANTS 



171 



tu tlw <liu I'm in, .Dal by adopts an oplieal 
method and thus obviuto.s tin: [lOHsiljiliLy of 
inertia, errora. 

'J'ho spring-piece W, awn in -/''/. 00, in 
hollow and in connected (it its upper end to 
the ehaoklo A of. tlio lasting machine. A 




Fia. 81). 



projection through the shut'klo is mounted in 
11 light-tight bus B, Tho ray from a point of 
light X is rotloetod by a fixed mirror Q on 
to a concave- mirror M, which again reflects 
'it on to a third mirror N and thon.ec to a 
photographic plato at V, whoro it ia accurately 
[ooiissed. 

Tho mirror M IH mipportccl on three points; 
two of thcso, about which the mirror can tilt, 
nro in emit not with tlio hollow spring-bar, 
while tho third rests on a cup on Iho top of 
the central rod T. Any stretch of the spring- 
bar W will emiao it ti> move relatively to the 
(seiilral rod T and thus tilt the mirror JI. 
This tilt will niuiRO tlio point 1? to movo 
horiwnitally across the photographio plate, 
a distance "f 3*0 tinica tho stretch of tho bar. 

Tho mirror N is rotated by the link work 
0, L, V, U proportionally to tho stretch of 
tho teat piece between tho gaiigis hsngfch <jf, 
and this inovemont diaplacea the point "I" 1 " 
vertically up nml down on tho photogi'aphio 
plato. The point of light therefore traces on 
tho plain a atrtiaa-atraiii diagram of tho teat 



nnulo. AfltM' dtivdopnicnt the irlaiimi bi;- 
tvveon hii.nl and oNfeiiKion c-un he* ]iH-iiHan'il 
from (.lui pliilt! wilJigi-Cftt iiL-miracy. 



V. DETKriMlNA'I'lON OF TIM) 
CON.S'I'AKTS 

Tho compkitn load - oxtnimion diagram in 
drawn by menus of sonic form of aulognvpliic 
diagram apparatus, hut for tho iicounito dclnr- 
minatioii of tlie plastic limit and mmhihiH^if 
elasticity it is tifit'osnai-y I" diitcrrnino \vilb 
exl.roin accuracy (he deform ationH prodnisiid 
by sninll hiadw. 

(02) Till': KLABTIO LIMIT. ..... The i-lnKlu! limits 

in tension and (soniprcHHimi <blninnd from Hlrt! 
atrain CULTCH on the first Iniiding of a jiiotio of 
material sucli RH steel urn not constant for tin* 
material hut depotid upon tlio provioua trc-nt- 
ment tlmt the miitorial has undergone. Thoy 
ara called tlio " primitive " ohistie Him its tn 
distingiiiah them from tlio ll natural " o1antici 
limits'set up in tho material when it ie sub- 
jected to a few alternatioiiH of stress. 



M (Cancnva Mirror) 



Stutalife of 
Tasting Maohlna 




-T 

W {Spring Pleea) 



raat Piaco 



Fid. 00. 



Tho definition of tho elastic limit which luia 

been standardised by 1i " '""Si^i, i.ir---- : 

Staiuliu-ds Assjociix 11 ' 
acceptctl in this c 
least stress at \vbic. 
ho oxaet, Tl, is Bomci..... 
proportionality or tho " 1: 

With some matoriald thoro ..= , 

II.()oko'fl Law, und a la'ok of )..,-, ., 

between stress and strain, ovon for valnca of 



172 



EL A STTO CONSTANTS 



the strosa HO finiall that; when it is removed 
thi> inaturial regains its oriyimil dimensions 
(i.e. Mint thoro in no pui'iiLanoiit wef.). .Hence 
tho elastic limit is onc-asmM-illy defined us tho 
maximum stress below which tho material 
would fully recover its foi'iu upon removal of 
tho liiad. Thin may lie willed tho "11" .Limit. 
With must iiifiloriiila the two definitions (five 
substantially the same results, ilioy lioth re- 
quire delicate extenmmietera for their deter- 
mination, but tho motlmd of procedure during 
thi) test is slijflifly (lilYorenfc. 

In tho first case ex (clinometer readings uro 
taken with gradually increasing loads find the 
rcsulla plotltid 'H a load extension diagram. 
This point at \vhieh them is a deviation from 
Hnoko's La\via easily located, ami the Modulus 
of Elasticity eiin bo calculated from tho slope 
(if the elastic line. Tho increments of load 
taken nro uaunlly about j' s of tho estimated 
value of tho " 1* " Limit, mid if the valuo of 




3 Q 1O 12 11 10 1Q 20 22 

Stress In Tana /ie>' air- In, 
Via. 01. 

tho " I? " limit is known to a first approxima- 
tion, thcs intsronients are made nnialler in tho 
noi^hbfiiirlidod of that value and until (he tost 
is tinmpkiloil. 

The fi)llowius tneaNitremeiilH {'I'alili! i^l) are 
taken from a Hjiiiiiitin'ii niadhinecl from a pieoo 
of Jioilor plato and slir>w how tlio " 1' " limit 
and tho modulus of elasticity ran be calculated. 

'J'ho re-sultH are plottoil in Fly* 91 and show 
that tho limit of pnmortionality is at 1(1 tons 
per sijimi'G inch, 

Ifrtnn tho olnstie lino it can ho scon that at 
a stress of li)-ti tons por Hmiavo inch the ox- 
tonsomotor voading is 2fi4; thia is nnuivalont 
to nn extension of 0-001 in. on 1-0 in, 

Tho strain ia therefore 0-001 and the modulus 



= 18300 tonn/flii- in. 
:---=29-8xlOlba. por sq. in, 

If tho rend i tigs of tho extension nnd tho 
Inad am known to suffidont aoenraey, 
tfio limit of pi'(i|)orti"iiality ean lie aHenrtained 
witli moro nrcusision hy ealeidating tho elastic 
oxtciiHion for tho various loads applied, and 
plotting tho difference between tins and tho 



actual extension as ordinatos with tho louds 
as ulwcifiMiU 1 . 'I'aMo 21 shows this cali'iilutioii, 
and tho results aro jilotfod in Fi</. 02. 

TAJU,I: 2t 

EXTEKSOMETEIl TllST ON JioILKIl Pf,ATK 

Diiuiitstor of U-al |iieci'=0-;i75 in. ; Orosrf-Kcotionnl 
ai'i?u=0'1104 Kt\, in. K.\t(!iiHii)n!' mcAsniml mi 
n l-inch Range length !iy n mirror oxti'tiHomclci-. 



' 

H tress In 
Tons per 


ICxtcil.ilon 


Cnlnttlatcil 


'' Sot" 


Sit, In, 


A. 


liiXteimion.* 
.!!. 


A -II. 


O'OO 











0-14 


8 


8 





0-80 


Ifi 


17 


2 


1 .;!,'! 


27 


2(1 


1 


1-78 


35 


3J 


1 


2-23 


11 


<ll 





2-08 


BO 


51 


1 


.1-13 


57 


50 


_ 2 


;i-57 


(17 


(18 


- 1 


4 '01 


74 


7(i 


2 


4-4ti 


83 


85 


... 2 


fi'H. r 


101 


102 


1 


(S-24 


117 


110 


_ > 


7-U 


134 


i;iii 


2 


8-OIJ 


150 


153 


-!! 


8 'SKI 


1(1!) 


171 


2 


0-82 


188 


18H 





10-70 


20(1 


2011 





11 'fit) 


221 


22;( 


- 2 


12-4(1 


2:17 


2-10 


-II 


111 -.'18 


253 


257 


~,l 


14-27 


272 


27-1 





15-17 


21K) 


21)1 


- 1 


lli-Ofi 


M8 


308 





10-03 


:t;io 


325 


r> 


17-81 


3&;j 


IMS 


n 


18-73 


3H3 


;i5ii 


2-1 


liH(2 


: HU '' 


.-.. :17(1 .... 


H5 



' I mill-" 1/25 1,11(10 In.; i.r-, 'Wl iliills^U 01SI la 
.Results of ti'rtlsi; 

l^liiHiiii limit--- Hid (,oi):i/Hi|. in, 

Ultimate Htivus Srt'O'l (.IHW/HI'. in. 
Mfiilnhm f claht,1(!ity = 21)-8>: III" Ilw./Hri. In. 
l'!x(.i!iisf(m = !J(H) |ici; i:cn(,. 

..100 



^fi CO 



iTTji 



'IE/HI 



ttatlmtt 



O fl 4 tl D 10 12 14 1(1 10 QO 32 

Stress In Tons par sq. In. 
Flo. OB, 

It ifi of first importance that shoeks and 
vibrations should bo avoided (liivimj the appli- 
cation of tho load in an oxtoiiHometer lest, 
sinco notions of tiiis kind msi'lmisly alVect the 
aonsitivity and tho accuracy of tho instrument. 



ELASTIC CONSTANTS 



173 



The Mdfioncl method nf procedure, employed 
to determine the " II" limit, is to apply nil 
increment (it llio loud and upon its release 
measure tlio amount of tho permanent act, 
if any. Tho loud is then doubled, and the sat 
on release again measured. A further increase 
of tho lone! is applied anil released, mid tho 
operation repeated, until a well-dofiued anil 
inonmsing permanent sot is obtained, 

Tho amount of the permanent sot is plotted 
against the load and nn estimate obtained, 
from the curve, of tho point at which the 
m ntorial starts to have n permanent set, 
.From this reading tho "R" limit is calculated. 
'Results show tliat the actual location of tho 
elastic limit depends on the sensitiveness of 
the apparatus used, low results being obtained 
with instruments nf high sensitivity. Tho 
determination of tho " 11" limit requires eon- 
aidc.rahlo time to cany out, but indicates 
plastic yielding of the material at an early 
point when it is properly ascertained. 

(i.) JUnstin Limit by Change, of 't^.i/iperalnre. 
if a maloriiil behaves elaslicnlly, increasing load 
prodnocs a cooling of tho test piece, but if, 
however, n permanent sot is produced, vorl< 
is done in internal friction and tho tempera- 
ture of lh test pieco rises. ~K. Knsch, 1 ti 
Cjross Lichtorfeldc, 1ms earriud out some ex- 
periments to determine tho temperature -loud 
curve for materials. Vor temperature meas- 
urement he uses thormo-tniujiles nf iron-con- 
stn.n(.ft, copper-con stun tan, ov nilver-c?onslan- 
lim bound to tlio test piece. Alterations of 
Uio temperature arc read from the movement 
of 11 galvanometer. Ho limlu wcll-doiiiHid 
points of inflection in his curves. Tho loads at 
whicih those points oecur give- (in elastic limit 
sometimes called the thermal or " T " limit. 

(ii.) Effect nf Overstrain UH Elastic Limit and 
Yield 1 'oin (. Jiausel linger found tho effect, on 
tho limit of proportionality, of overstrain to he 
119 follows : 

(1) If tho limit of propnrtiotmlity was ex- 
ceeded but not the yield point, then l\v> former 
is raifted oven if the tost piece is immediately 
roll Hided. 

(1!) IE the yield point is exemlcd, immediate 
reloading gives a lower limit of propnrii'maliti/, 
but ndoafl'inf! nEter a long interval (if time mny 
{jfivo a rniscd limit of proportionality. Jamca 
Muir 2 found that this efl'cot can be accelerated 
by immersion for a fmv minutes in boiling 
witter. 

Bauschiiigor also found thai tlio effect on 
Ifia yield paint was that if tlio yield point was 
exceeded, then subsequent reloading gave a 
new yisl'l point raided to tho stress to which 
the liar wns londed in the firat place. This 
ufl'cot occurred oven if the liar wns rdoadci 
immediately, but if there was an appreciable 

' I'rori. Int. Assw. Tfsl. M<tl., 1001),. Attlclo vi!,. 
3 Rov. A'oc. Wril< Trrtns., 1000, cxdli. 1. 



nterval of time before the reloading this new 
ield point might be higher thsui the maximum 
stress applied in the first loading. 

(03) TUB MODULUS OP EiASTic-m'. 3 The 
iiodnlns of elasticity is tho number by which 
JIG amount of any specified stress or component 
of a stress within the limits of elasticity must 
)o divided to find the strain or any staled 
3innponout of the strain which it produces. 

There is a modulus of elasticity in tension, 
sompressinn, and shear. 

Tho modulus of elasticity in tension, denoted 
>y K, is sometimes called the modulus of. 
direct elasticity, or Young's modulus. Tho 
value in compression is i/cncmlly the .samo us 
..hat in tension. 

Tho modulus of elasticity in slicnr, denoted 
jy 0, is Cidleil the modulus, of tnuisvei.-so 
Insticity, or the modulus of rigidity. 

Tho moduli G and K arc connected by 
..hu equation 



where a Toissoii'n ratio, 

There is nlsu a volumetric modulus (if 
elasticity, sometimes called modulus of elas- 
tieity of bulk or inoduhis of culiic compressi- 
bility and deciotwl liyK Jt is tlieninnhm 1 by 
which tho stress upon the exterior of the mib- 
Mtance must be divided to give the diminution 
in volunui or ciiliicjil sirain. 

If F, and f ! iii'c !iiio\rii, 1C am bo (ssiluulfitcd 
from tho formula : 

CE ., 13 



g(G4) MODULUS ov Uinno p e KLASTIOITY. 
An example of tho mothod of determining tho 
modulus of direct elasticity (K) in given in 
g (02), Some materials, e.y. cast iron, nun-tn-r^ 
and cjonorete, have no clastic lino and therefore 
no definite modulus of direct elasticity. It can, 
however, bo considered to he tho reciprocal of 
the slope of tho stress-strain curve a.t v.cro 
stress, hut where the curvature near the origin 
is sharp this value of the modulus is of littlo 
use exoojit as a comparative, value nf stiffness. 

An cxn.mp.le of n stress-strain curvo with no 
definito clastic 15iio is given in Fig. !)3. Tho 
initial mwhilua of direct elnfilhsity IB olitained 
from tho slope of the tangent (DA) to the 
curve at tho origin. 

For concrete, nn empirical modulus is some- 
times used for design (.'idculations. Tho value 
is obtained in one of three ways : 

(i. ) The " tangoist " modulus (E,) is obtained 
from the slope of the tangent to tho stress - 
strain curve where tho ordinato is the working 
stress 25 per cent of the coinpressivo strength 
ia usual for tho working stress that ia, from 
tho tangent CD (Fig. 93). 

3 Sco "Elasticity, Theory of," <f>). 



174 



ELASTIC CONSTANTS 



(ii.) The " eiHsaiit " modulus (H N ) is obtained 
from the slope nf the lino 0.15, where JM-the 
working stress of (lie material. 

(iii.) The " ehord " modulus (K (1 ), determined 
hy the ratio of stress 1o deformation, is given 
by the chord drawn liel\ram t.wo points on tho 
ciirvo, defined by tlio limits nf stress for work- 
ing loads, i.e. from the chord El*' (fig, 9i)). 

'['lie tangent anil ohord methods give moduli 
of approximately the sumc value, whieh are 
higher than tho secant modulus, 

Rtfuiton Walker 1 has shown, from a study 
of curves which ho obtained from various 
samples, (hat tho stress-strum curve its repre- 
sented by a enrvo of tlio typo 



wliere, S unit strosa in coucroto, 
rf=.-iiiii of deformation, 
K --rioiiHttint do|)cndinu; on 
=-an iipin-oximutol 

nnd the I'clation bctwoon n 
and strength of (joncrolo in 



of eliialioity 



Jlatfirlul 



where JS^ modulus of elasticity, 

C-cnnstiint depending on conditions 

of test, 

S = comprcssivo strengtb of concrete, 
wi^un exponent. 

Similar eolations were suggested by 
and Morsel). 3 

Itlffed of OvKrtitraiti on the Ufatlulufi 
Direct ]$I<i$t!cili}.~]f the limit 
of proportionality is exceeded 
the valno of E for steel is 
lowered, in Home cases as 
much as 20 per eent. Re- 
covery, however, is eficclctl 
by rest or immersion in boiling 
ivater. 

Marshall a .showed that if 
steel IH initially strained to a 
point within the limit of pro- 
portionality, a second loading 
may give slightly biher values 
of IS.' 

((15) VALUES oi' THE MODU- 
LUS op DIRUCT ELASTICITY 
(Yniiwfs Mothtlufi).-~'Vm car- 
lion steels tho value of lil in 
His. per fsqiinro inch varies bo- 
tween 28'fi x !() and 31 x 10 8 , 
witb an average) vabia of 
29'0xl0. It is nearly tho 
HIDIIO in tension and comprcs- 
Hion, and is (imcticnlly in- 
dependent of the carbon oontont and of tho 
beat treatment. 



h'or low 
eent) tho 
Ibs. ]icr flqiifu-o itui 
for high porcoutitgi 



M irK,,| 



,{ t 




per cent) is low, lioinj,' it I 

Kfjiniro inch. 

U'ith cast iron (Imrn i'i in. 
of olnslieity. UHIII^ a \ntil, 
l(t,()(10 11)3, ]ier wijmiM' in- I 
inodiilua for oHt iron vmn 
20 x 10 Ibs. pur mi[iMi]-e iin b 



TABIJ-I iJ:i 
VALUES <n' TKH MODULI 



(.Virljon H[{?C!H . 

Low porticiiitiigft iiiplvol Kl ci; 

(.'nsl- iron (t, r ioy) 

fust iron (wliiln) 

Coj)]ii>i' (rolled) 
(_'o[)|ii;r (hard ilrnwn wiro) 
('oppor (nnacnUMl wire) . 
Alniiiiniiim . . , 
Thosphoi 1 hrou/,0 

Lead 

Timber (Englwb oak) , 

(KnHuinn lir) 

(CliriHtiniiin Hpriiei?] 
(hemlock) . 



Vntiitt of K. 
In, 



irh^ion.oni) 
]7,(HIIMHMI 



M.OOO.OIIII 



\;i,()i)(i,(nn) 

1, 5(10,0(111 

a.finiMHHt 



I], dimi-retf. Nteel Ouimlriidtiiii (translation 
Der Kisenlti'tonluiH), 




and from 20x1.0 tn ?.!> 
inch for while cast iron. 
Further values nf 'K m<< 
(00) MODULUS oi' 1 



li l 



TICITV, OR 

onsiest method (if 



ELASTIC CONSTANTS 



liy mcaiiK <if a turmoil tost. Tho strain in 
by Homo form of torquometor m;h 
iti (55). 

A stri'Ss-Kl.raiu tliiigrmn JH drawn in the sanio 
\\~ny as for direct stress but Imving toraiomil 
HfcrosH na aliNisiwn and torsifintil strain ns or- 
dinate. The vfiliio nf is then calculated from 
Hit) slnpn of t!io clnstii! Hn. The elastic limit 
in shear is nlflo onsily located from the curve. 

A Hurics! of observations by tiic JiT.P.L. 
mirror toriniemefer ( (55)) on a piece of a 
shaft arc given in Table 23 and the diagram 
nlmwn in A7r/. 1)4. From this diagram the 
limit of proportionality in eh ear is Rcon to lie 
with a torquo of 1360 Ibo.-in. corresponding 
to a stress of 24'0 tons per square inch, anil 



2QOO 
200 O 
2400 

'5 2200 
bi 

.2J20OO 

V 
t- 1000 
a 

.C 
-|j MOD 

iiooo 

| 

GOO 
rtOO 
flOO 



















, 


















/ 


















/ 


















tit 














__ 








- 























/ 


jf- 


















x 


/ 






r 


/ 








r~s 


7 

















-=- 


































JO 40O GOO UOO 1O0012D014001QOD10OO 

Torque in lbs-li>3> 



"Eia, 



tho motliiliifl of rigidity' (0) = 11 -9 x 10 Ibs. per 
square inch, 



-=- OxlO]l M . porsq. in. 

strain 0-00463 1 

J Y / ._Stvcss= 24'0 x 22'10 llin. per sq. in. 
~r>;t,800 Ibs. pcr.sii. in. 

/ where ) = ratlins of tho test 



piece, 

= angle of twist on 
length L in 



Strain = rO/L 



= (0-25 X 4-Jfl)/(4 x C7-3) 

'For wire the valno of is determined from 
the time of a single toraioiml oscillation. 
JJaufichiuger 1 found the valno of for 

1 Givilitigciiiatr, 1878, 



sice! of cnrbon content varying 
from 0-1!) per cent to O'flfi per cent to rani-i) 
from ]l-)xlf) to 12-7x10 llis. per ^quiiro 
inch, 

Plntt and Hay ward * give values varying 
from 12-3xlO B to 1-4 -Ox 10 Ibs. per square) 
inch. 

Average values of arc given in Table 22. 

(67) POISSON'S RATIO, Poisson's rafciu JH 
the ratio of lateral to longitudinal doftirnwiflnn, 
and is usually denoted by IF. 

An pxtenaometcr when used in conjunction 
with an ap]iaratns for measuring lateral utrnins, 
such as are gjpcn in (67), gives the value 

TABM: 23 

TonstoxAL STKESS-STBAIN OBSERVATIONS 

Diameter of test picco=0'fiOO iimhea, 

flange lengtb='l iiiehc?. 



Twiatiim 
3 In me lit. 
Lbs.-Ins. 


Toraional .Strain. 


In Torquemcter 
Tlnits." 


Anglo. 


100 


Ill 


1!)' 


200 


2i>o 


US' 


300 


320 


07' 


400 


M2 


1 Hi' 


fiOO 


r>fil 


1 :u' 


COO 


050 


1IJ2' 


700 


709 


!> a 12' 


aoo 


880 


2 3 31' 


iWO 


DH'J 


2" MY 


1000 


1103 


;I Q ' 


Hl-iO 


IMS 


;j u id' 


1080 


a 100 


3 23' 


1120 


12113 


a si' 


1160 


1278 


3 3D' 


1200 


1322 


3 40' 


1240 


1300 


3 D (31' 


1280 


1-!03 


3 fiO' 


1320 


M-lfi 


4 Q 7' 


1360 


1407 


4 a 15' 


MOO 


IBSO 


4 2(3' 


1500 


1C01) 


i" r>o' 


IfiOO 


1910 


5 2ft' 


1700 


22-10 


G20' 


1SOO 


2859 * 


7 58' 



* A rc.idlng of 2850=nn niifrlo of twist of 7 ilrKrc.'it 
58 minutes on a length of -1 inches. 

of o- for any material in tho most direct way 
possible. 

Both instruments are flxutl on tho tcist 
piece at tho same time and moaaarcmontH arc 
obtained, <>E both lateral and Inngituiltunl 
strains, for equal incromenta of lontl. 'J'lm 
results arc then plotted ns stress-slnim dia- 
grams, and the laiio of the slopes of. the 
clastic lines is oqnnl to a (Poisaon's ratio"). 

The figures in tlio following table arc taken 
from results obtained "by Ci>hcr. 




17fi 



ELASTIC CONSTANTS 



that materials fail under stresses ei 
lower than tho ultimate when those : 
^repeated many times. 

1 Stanton and Bairstow 1 have shown micro- 
ncopicidly that this deterioration is due to 
"slip lines being net up at the point of maxi- 
Jiuiin stress in the cleavage planes of tlie 
crystals and duo to unequal distribution of 
stress among the crystals." Those slip lines 
broaden ovit and develop into actual cracks 
under repetition of stress. This type of 
failure is sometimes called "fatigue," but is 
perhaps better described tis a " repealed stress 
failure." 

In many cases the stress does not alternate 
between /.ero mid a maximum in tension; 

.I'Yom the plotted values of those, results there may bo an initial teimilo or initial coin- 
given in /'/;/. Oil it will ho noted that tho pmssivo stress. For the purpose of a con- 
curves do not piiss tlimugli the Jir.st point, but sideration of this subject eomprosHivo stress 
the remainder of tlio observations lie on is taken as a negative tensilo stress, and the 

range of stress us the 
dill'oroiieo between tho 
maximum and minimum 



Jionil In [Jit;. 


Lnt i>rnl Hlniln 
Henillnj;, 


ViOimM.uilimil Strain 


1,001) 








3,000 


20 


34 


fi.OOO 


4-2 


(ili 


7,000 


03 


ill) 


9,000 


fi!i 


132 


11,000 


10(1 


1M 



Slapa ol Lateral St-ain Stress C.uiaa = ^ 




iaoo MOD 3ioo 4oon .in no no no 04 DO 7900 oooo nnoo DOOD 10400 moo 
ionrf In Ilia on i'01 Ins. cllaiu. 
FiG. 05. 



straight lines. The slope of the longitudinal 
slross.sli'aLii ciirvo --'108-7 x 1.0- lu , and Mto slope 
i)f tlio Intend atroas'-.Hl j-jiiii ui'vo = 107 x IO- 1D , 



n's ratio for vnritma 



Dulta innlul 
Muntx met ill 
Lent! . 
fit 01 10 

(Vmm'cfo . 
(-'iiHt iron . 
Wrought iron 



Vllllll) (If I'lllH'iDll'H Ittltlo. 



0-27 to 0-30 

0.33 (0-31 to 0-!W) 

0-3, 1 ! (0-32 to 0-3B) 

0-34 

0-34 

0-L>() to 0-3't 
0-08 lu 0-18 
0-L';i to 0-27 
0--21 Lo 0-20 



VI. Sriwur, .FOHMS OF TEST 

ON Til K 11 HI'ETITION OF 



A Ittiriuttintf Htresses arc 
usually isonsidonsd as lie- 
ing those in \vliioh tho 
maximiim and miniiniim 
ntresHes are (.'([iial hut of 
opposite HI^JI. 

Sinms IH'i'l, when Ji'uir- 
bnim iniblishod resiillH in 
the Ho//, iSVxr. J'/iil. '/'num. 
on riveted wrought iron 
girders subjected to re- 
pealed stresses, many im- 
portant researches on this 
subject have luicn, under- 
taken. An a result of his work, h'airbnini 
rcuom mended that the Biifo i-ojiontud stross 
should bo not more- than one-third of Mm 
ultimate stress. 

In 1S71 Wiililor imlilished tin; ivsidts of an 
oxhaiiHttve series of repealed HtrenH (experi- 
ments in direct stress, bonding, and torsion 
which had biien (sarriorl out during the previous 
twelve yearn. A full dcseriptiun of thiwe tests 
is given in Eiigine.Krm<j of 1H71, and a good 
account by Unwin. 3 Tlio most important 
deductions from these oxporimentH on wrought 
iron and steel are ; 

(.) A stress below the ultimate will fracture 
wrought iron and steel if it is repeated many 
times. 

(b) Tho range of stress, and not tho maximum 
stress, determines within certain limits tho 
nmnbor of repetitions boforo fracture. 

(c) For a given maximum or minimum stress 
tho number of repetitions before fracture 
increases as tho range ot stress is diminished, 

" Hcalstnnco nf Tron nnil Stool to IlovofHiils I 

7H. 
1010, p. 371 



ELASTIC) CONSTANTS 



177 



nml there is 11 range of filross called 

runfjR at which the number <>f repetitions is 

infinite. 

((/) The limiting range of sti'OHS diminishes na 
the maximum Hf.rosrf incrcaura. 

Wohlor's work wan (.-on tinned (in tlio twine 
machines mid confirmed by R[mngcn!.u)r|j, 
ivlioae results, however, ivore not no consistent 
as tlio original work by Wohler. 

.Re.sultH published in ISSli by Hakor, 1 who 
liaii experimented wilh soft and hard Hfeel 
(JJ8 and !- tuns per square inch respectively) 
and 27-ton rivet iron, won; in uomjikilo ngrce- 
inent with Wohlor'.i roHoiu'ehost 

A (ionsidoiublo nunibor of: experiments on 
Ihu effect of varying values of (ho minimum 
streaH on Iho limiting rango of stress have been 
curried out by [faigh, 3 

.In IfUfl ho reported a series of tests on mild 
steol to the British Awsouiation. These- are 
Hummtii'iaed in Table 20. 



Ulthuato 

Stiltll! 

Htross. 



20-0 



LiiniUug 



- -1-05 

- 0-88 

- 7-3 
- 13-0 

- 1(1-11(1 
-20-10 
-21-05 



Li ml linn 
Maximum 


LimltlMR 


TOIIH/HH. In. 
11. 


It-A.' 


H-Sl-fifi 


17-fi 


-1-20 -R'2 


2].fi 


-1-1 7 -20 


2.1-5 


-1-1 It -00 


2(i-0 


I- li-51 


2,'t'fi 


-I- 1-10 


2l-r, 


- 2-lfl 


ID-fi 



Tlio I'uaulta are plotted in Jf''iV/. 9ii, from whieli 
it is seen that 

(1) When tho miiiinunn strcHS in v.ero, tlio 
range of stress is approximately 21-0 tons por 




-24 -20 -1O-12 -0 -H O 4 H 12 1(J 2O 24 QQ 

Minimum Stress In Tons peeaq,in, 
I'KI. 00. 

square inch, i.e. a tensile stress of 80 per cent of 
the ultimate stress is suiTieiont to fnioturo the 
material when repeated a eontmlorablc nninbor 
of times. 



1 " Notns on the WorltlnR fitrcttrt of Iron und 
titoul." Amer. tioo. Mccti, Jinn, Proc,, 18M. 

a Jtrit. Assae, Jtciwrt, 11115, p. 1(33; alao Jtttl of 
Metals, 1., 1 1H 7, No. 2, p, 6D. 



(2) \Vhen the minimum stress) is IC-HS Minn. 
half of the rane (i.e. from -i-05 in- IH-0) the. 
curve approximately follows (ferliot' 1 
(MOO (7(1) (ii,), othorwiwo there in a 
deviation from the parabolic form. 

licsults in Tnblo 27 givo defailsi of tho 
oli.acrvat.ionH on mild steel when Mu! H(.I'(!KS(SH 
fii'O alturnntinj' (i.e. equal tiiiiainn ii<l I'om- 
prosjiion}. 'i'lie^e eonh'rrn Woliler's dodudtiotitj 
b and c, given above. 



limiting riinun of H(.i'CKs~~^(i-0 loim iici 1 HO. in. 




Ultlmiiti) 
(HlnMiO 

ToilH/iSl). J II. 


Altonwllnj! KttvHsrH. 

{IClllllll TollMlll) llllll (J(llllJ)H'anloil,) 


Kiintfo i>f Stress, 
ToiiH.Wq. In. 


tol'riintmi'. 


26-0 


39-11 * 


o-oo;! 




,. 1)2-7 


0-08 




31-3 


(M)flll 




111 -3 


0-lli 




20-0 


0-1 11 




21)-!) 


0-BO 




28-8 


0-!1 




28-7 


1-01 




7'Tl 


1-117 




2<H 


2-18 


Tests on 
iiiHi'ifMHt in ' 
and show tha 


25-1 


7^1 1 


Vaval BniftH by Jlniu.li jiro mini 
'abki 12S and plotted in Fit/. 1(5 
t for the lira MM midiM'uniuiidi'i'Rl.ioi 


the equation cimuecfing minimuiu H(.ITH:I IIIK 



TAHIJ-! 28 

ItKl'BATUH LOAIHNO 1'KH'i'S ON NAVAL F)ll,1f(!l 



mt.limito 
Sirens. 
(Statlii.) 

I)llM/H(i. 111. 


I.I ml M UK 

fitniiis. 
TraiM/Hq, In. 


Limiting 
Maximum 

TI>HM/SI|..[II. 
Jl. 


Llmltli 


28-7 


- 1-0 


-1-1(1-5 


17-5 




- ;f4 


-|-lf>-8 


lll-i! 




- (1-f) 


-l-W-5 


ai-u 




- 32-0 


-1-12-0 


U'l't) 




^17-0 


' -1-10-5 


27-1 




-20-fi 


' 8 ' r> 


2IJ.I) 



rftngo of stress in that of a Hli'ii.ihl lino p 
throiiffli the point whore the minimum 
iw equal to the ultimate sli'CHH. lluiyli miyn Unit, 
fifi a rule, metals which give a fiummlui'iiblo 
reduction of area at fracture have a hij^Ji vnltio 
ot the ratio o[ alternating strong mn#o (with 
erLiial tension und emnpreHHion) to tho ultiniuto 
stress), This usually varies betwei^ii 1-20 in 
ingot iron and tho besit niild stool imcl 0-80 



VOL. I 



178 



ELASTIC CONSTANTS 



in high tensile ami tool steels in the annealed 
condition. 

g (01)} BAUHCHINOER'S Tnuaity OF FAILURE. 
Bauschinger's theory of failure fine to re- 
pented stresses is tho only one which 1ms 
received serious consideration. Ho shows that, 
with burs subjected to cyclical variations of 
stress, the elastic limits in tension and compres- 
sion take up new positions, tho range between 
the two limits depending on tho material and 
tho stress at the lower limit of elasticity^ Thus 
if the elastic limit ia rained in tension by 
overstrain it is simultaneously lowered in 
compression, HO that for that condition of 
loading two now limits are sot up, which 
Bauschingor calls tho natural elastic limits. 
Ho showed, further, that the range between 
these limits was tho same in magnitude as 
the maximum range of stress which could ho 
applied to tho material an infinite number of 
times without causing fracture. 

.IJuirstow, 1 in n important jmpor communi- 
cated to tho Koyal Society from tho N.P.L., 
has given experimental results which con- 
stitute tho first strong support of Bauschinger's 
hypotheses. 

' In tho testing machine, used by Uairsl'ow for 
tho purpose of tho experiments, cyclical 
variations of direct stress aro automatically 
produced at tho rate- of two por minute- in 
Riich n manner that tho extonsomoter, which 
is of the Martens mirror type, is fixed to tho 
specimen throughout tho test, and in this way 
tho whole history of the progress of fatigue ia 
observed. 

When tho limits of stress arc tension and 
compression of equal values it is found that, 
if the range of stress is above a definite 
value, tho stress-deformation curve forms a 
closed loop, which is called tho hysteresis 
loop, consisting of two parallel straight lines, 
corresponding to the variation of stress from 
tho limits of stress towards tho mean stress, 
and two curved portions, corresponding to 
tho variations of stress from tho inonn value 
to tho extreme values (J%. 97). Tho width 
of this loop, which is tho permanent set of 
the specimen por oyolo, increases aa tho range 
of stress increases, but for a definite range of 
stress tends to a limit which is not greatly 
exceeded by subsequent repetitions of loading, 
oven when this ia tho range at which fracture 
under fatigue eventually takes placo. Undoi 
these conditions of stress tho mean length of 
tho specimen remains constant. 

When the limits of stress arc unequal tho 
hysteresis loop ia formed as before, but is no) 
cfosod, owing to tho fact that tho mean length 
of tho specimen gradually changes because o! 
tho continued repetition of tho same cycle 01 
stress, i.e. the change of mean length of the 
Hpcoimcn per cycle is tho amount by which 
1 Boy, Hoc. Phil, Trans. Sorlus A, cox. 3G-5fi. 



the hysteresis loop is enclosed. Tho amount 
of tho permanent extension during tho earlier 
stages of the breakdown becomes considerable 
tho superior limit of stress approaches 
tho static yield point, and if its value, after 
tho first considerable stretch has occurred, bo 
plotted against tho corresponding values of 




f Loop 



-10 o +10 -tao 

Stress Tons par si/. In. 
Via. 07. 

tho superior limit, it is found that tho curves 
gradually come into coincidence with tho 
ordinary static " stress-elongation " curve at 
tho yield point. JiMiABG (Fiy, 1)8} shows 
Hiioh a curve, in producing which no cyolieivl 
variations of stress are concerned. 

Tho principal conclusions arrived at by 
Bairstow aro summarised thus : 

() The " natural elastic range " is tho valuo 
to bo used in design, and, with equal emu. 
pressivo and tensilo stresses, this valuo \a 
identical with tho " Wohlor safe range." 

(b) Tho natural elastic rango depends upon 
(1) the material and (2) the lower limit of 



10 




Axle Steel 



o-a O"i o-Q O'O 

Extension- IHilllmalrea 

Fid. 08. 

stress, Tho elastic rango when tho lower 
limit is KOI-O is less than that with equal tensilo 
and comprossivo stresses (about If) por cent with 
axle stcol and per cent with Ucdsomor stool). 
(c) If a stress-extension curve is plotted, 
tho extension being the valuo of tho per- 
manent extension reached after repeated 
alternations, it assumes tho form found with 
hard drawn copper wire, which has no yield 
point but corresponds with tho curve FKJITJK! 
of Wig. 98 produced back to tho "natural" 
clastic limit, 



ELASTIC CONSTANTS 



171) 



(d) Recovery duo to stoppage of tlio alterna- 
tions of Hirers is appreciable, being somewhat 
rapid for Homo materials. Recovery reduces 
tho permanent extension (it a given loud and 
ran bo greatly accelerated by immersing in 
boiling water for n few minutes, us suggested 
by Mnir. 1 

If an meliiKvl lino a^t (Vig. 09) is taken to 
represent the limiting minimum stresses, and 
the limiting maximum stress corresponding 
to each limiting minimum stress is plotted 
on the corresponding ordinmle, a curve of 
maximum stress ea is obtained. The vortical 
distance between the two curves represents 
the limiting range at stress ntul it will bo 
observed 

(1) That H3 tho limiting nn'nimnm stress 
increases tho range dccronsos. 

(2) That if both tho maximum and minimum 
stress applied to tho material fall between tho 
two curves, then tho material will not fail 
under a repeated stress having those maximum 
and minimum values. 

(70) FORMULAE FOR RKPKATEB STBIISS 
TESTS. Various empirical formulae have been 



430 



-20 





Tha curves ivaro obtained by 
plotting ttii results glaeu Inj 
a mild steal 



Fid. 01). 

suggested to connect the limiting values of 

tho maximum, minimum, and range of stress. 

(i.) Wci/raugfi and Lminhardtfs Formulae, 

If / limXi =liiniting maximum stress, 
/,! ^limiting minimum stress, 

/^ultimate static stress, 
7*1 = limiting ran go of stress when / m | ni =0, 
23 a = limiting range of stress ivheii /, nl i u 
=3 f 

' noil, Koa. Phil. Tram,, 1000, oxcill. 1 ; nlao Roy. 
Soe. 1'roe., lOQO.lxvll. 401. 



Wcyrangh 2 suggested tfic formula 

f _ <7 J I"!"' C7 7 \ 

Jinn*. A - -f~(Ai ~ Ay), 
Jlinil;, 

whore tho stress is wholly or parfcty rovoraod. 
Laimliardt s suggested llio fonnutn. 



where tlio Htro.ya is applied without rovoiml, 
Fig. 100 is drawn plotting the values of /,,. 




-30 



Via. WO. 



from tho above formulae assuming tlio valmiH 
of /inin. t" u 'o on the- inclined lino ES and 



Tho latter have bcnn found to bo 
values for a variety of materials. 

Tho curved lino for tha nmxiTnuni 
limit derived from AA'cyraugh and LannhardL'n 
forinulno is sometimes assumed to bo straight, 
in which cnso one formula covers tho ivholo 
field of repeated stresses. 

(ii.) Qerbcr's Parabolic Relation, OorbiM' 
showed that, by plotting tho limiting minimum 
stress as abscissa and tlio corresponding mfii 
range nt) ordinato, a, ourvo was' obtnini'd 
which, to a first approximation, was para- 
bolic. 

Uainy tho provioua notation, Gerbor's 
bolio relation ia expressed by the fonnulii 



f.,,,, =' 

J 1IU*1 



niM. - /mill. .1. 



n being a constant for tho material. 

(71) IlEPBATI 

All Wohlcr's tests were cairlcd out tit 
of less than 100 reversals por ininuto, and n 
determination of tho fatigue range orjonpicd 
a very long time. 

' lust. Cii\ JiViff. 1'roe. Ixiil. 

3 Zeitseh, lies Arch.- utid Ing.-V ere'ins zit IfnnniH'ff, 
1873; nlso, Inst. Civ. Kny. J'roe., 1880-HI, Ulll 
280. 



ISO 



ELASTIC CONSTANTS 



Various machines have been constructed 
to accelerate tho tost. 

JJefuro describing those machines winch 
are in constant, use for this branch of testing, 
it is advisable to explain the usuiil procedure 
which is adopted in tlio determination of tlio 
limiting ran go of atrcaa. 

Starting with an unknown material and 
a machine giving 2000 reversals per minute, 
two method's of attacking tlio problem are 
used : 

(ft) If the amount of the material ia small 
mitl only n limited number of te.st pieces can 
bo prepared, a, low ranges is applied to the first 
test piece, which ia increased by about 30 per 
cent after ten million reversals. 'Increments 
of the mime value are added to tho stresa range 
after caeh additional ten million reversals 
until tlio test piece fails. (If the test piece in 
hollow tlio number of reversals nan bo reduced 



in order to ho satisfied that, if tho test pieco 
does nob break, tlio range applied is within the 
safe, range, 

Tlio machines which are in common IIKO ean 
bo divided into four main types : 

(i.) Rotating cantilever machines. 

(li.) Rotating bur machines with a short 
length under a constant bending moment. 

(iii.) Direct wtress machines. Load applied 
by an unbalanced revolving weight. 

(iv.) Direct stress machines. Load a])]ilied 
by the pull of an electromagnet excited by an 
alternating current. 

' Kami-sals 

o/ Banding *S7ras.s'. -This typo of machine ban 
been run successfully at JiOOO revolutions per 
ininnto and is shown diagramnmtieally in 
/''(';/. 101. It consists of a test pieco A hold 
in a rotating chuck 1> driven either dirait 
or through gearing by an electric motor ('. 



to leve mil- , 
linn,} The Counter ilrtoen , / 


iiuft Bearings 


\ 1 


1 




l ' Y "r>' IVorm-iulioel [f@]) 










' j--D 


to bo be- J^EjJlMJl 


; j-;:$- 


- 






" -4 p ., 


'^t 






J-" 


twcon two Attached to 
vithioi (us- ElcctriaM<itar(C) 


r 




f 


p. 
jf 




miming l!ii! \\\\\\ \X\\\ \\\\\\\\\!V 
material to ^\\\\\\\\\\\\\\\\V\\\ 


gear worhlny an 
ElBctr/eal cut out 




bo homo- 


\\ 






geneous). A second teat pieco is then in- 


\\ 






serted in tho machine and a range 


applied 


A; 






slightly higher than the lower of 


the two 


\\ 






previous values. This range in increased 


v> 






by small incrcmcntu (depending upon tho 


^v 


w p 


accuracy witli which the results are 


desired) 


X 


,_.L_J 


after each ten million reversals, until failure 





occurs. 
(6) Whor 



at least four test pieces uro 



available, lh linntiug range ist apjn'oacbed 
fnnii tho opposite direction. The first test 
piece has a high range of stress ii|>|ilic[l to it, 
and from the number of rcveiwds required 
(o fi'acliiro a.n estimate 1 can bo obtained as 
to (.he probfiMo range, '['lie noxt updcimen 
is tested vmdor 41 range still believed to be on 
the high side. 1 , and this proceed is ropeatcd 
until a- range is obtained under whioh the 
material does not break. A stress-reversals 
curve can thon be drawn, from whioh the 
ranj<e of atreas can ho estimated with what- 
ever accuracy ia required consistent with tho 
homogeneity of the material. 

The method of procedure adopted will 
dopond on 

(a) Tho amount of material available. 

(h) Tlio relative coat of preparation of test 
piecn and running of tho testing machine, 

(r,) The importance of the time of dumtion 

--'linos of higher speed than 2000 

it is iifnially considered 

' "ovorwafu is required 




W 



Fin. IIH. 



Tho lent piece is loaded by weight W on a 
scale pun H, which in attached (n the test 
piece through the ball hearing .1). Tho 
connection between the ball bearing and tho 
scale pun ia mioh that the latter can adjust 
itself in a vertical direction without putting 
any constraint on the ball bearing. 

Tho number, of alternations is recorded by 
a counter driven by a worm wheel from t\ 



worm cut on the machine shaft. The 

of tho test piceo usually operates a switch anil 

stops the motor ; by this moans the nwehiiuj 

ean bo run continuously with but littlo 

attention. 

A slight modification of the counting and 
stopping method is in some eases adopted. 
Tho counter ia attached to tho ball-bearing 
holder (by which tho load is applied) and ia 
driven by tho inner race of tlio ball bearing. 
The breaking of the tent pieco causes tho 
counter to ceaao recording, and tho machine 
continues to run, without a lent piece, until 
tho next period of inspection. 

A rotating cantilever machine- whioh has 



ELASTIC CONSTANTS 



181 



bcnn running snoccHsfidly at llio N.l'.U j 
whnwn in Ji'iy. 102. 

With a liomliiJK t"i'ti tlio Hii-rna rlistilbntion 
over tho croHH-soutum in unknown if tho oiantio 
limit is oxcDCtloil, and tho iinixininni 




fall* mi tho oiiLiii 1 lil>rM (if tho tost j>io<!. Tim 
lost |tioi!o isoftoit made, liollnw, IIH in /'Vi/. 103, 
tlio part under tti*l Iming only a thin alioll, 

Miuminos if tho nitating oantilfivor ur 
Wohlor lyjio havo boon iw<.:d fur ri'simrolu's 
dcHcrilmd liy Wfihlor, 1 Klond and liUshunlK, 8 
(J. .li. JJiHiioy, 8 .K Jiiig(U'H, J Stuntmi and 



(ii.) .Jiftldtinff Hni' i\f(tr.'/tiae..t. '.riun (..VJIK of 
iniinhiHo was lirsl. IIKIK! ly .Sdiulisniili.)!! 1 " in 
IHD2. '.I'lio nn;.noil uf trai, is Kliinvn cliunriini- 
inuUciiilly in /'';/. 101, Thn tiwl- 




I' id. llll. 



A'U()!> IH fluUjralcd tn a tinifori 
nionuMit ivliilo roviilvint' on ils sixin. .It in 
fiii])])nri.oil on awivdlin^ biinrin^ nl. A mid 
1), mill llio central |>orliui) bi>tw(!iui B and 




(! >H reduced in diuniohir. Tho maximum 

Htrt'MH (f x .) on t.bfi li'al. mrci! is wdmiln 

from llio 



Warn 
Mar.lt 

o-3i;t_ 

"JT: 


(o sii/f Testing , 1 
HO Glincli i 

\ " 7 ' 0-fO 


To fit \ f/Jnm. 
Ball Ocui'liig Centre Una of 
1 Ball Rearing 

O"(llain. \ 1 






L_'^__Z_Vt_J_J 




"' c "' 1 






J f iora/ 


*" 





/Minx, Bonding i 
wlioro tl ~ tho diiuni'teir of tlm riidinsi'd 



iStmdiM'Uikm" Hiiii 
iiictliucl of lis^il. hfin 
liccm lined liy J. I'). 
Ito wfir d lo a n d 
Kden, K'CiHo, and 




(iii.) Dircr.1 Nlri'^t 
MafJtinf.fi. 'l.nail 
liy ii.il iiu- 



.1. O. Koos," (!. 1C. Stromoyci-, 7 and 



. , 

They, uro niado oonnnoj'ciolly by Alfred J. 
Ainslcr & t!o., anil 'I'iniiiH Olson Ttssling Jlarliinn 
Co. Tho InUiii- (iinnjiaiiy eall thoni " Wliitc- 
Ronlhor imduiunco Icsliny machines." 

' I'liioiiifmiiff, li. 

1 I run awl Ntwl Tnnt. J., IDDi), Nit, 2. 

3 Iron itml Hterl Mi'lttllitruhl, J'Vli. J(KH. 

4 I run and filed Imt. ,!., UKIfj. 

' " ]'ls()orliiifi'iil.s (if SliviifUli ami l''al,luuo Pro- 
IwrtioH of \Vol(kd. Joints," Z6(. fJii\ Hug. I'm:.. 
11)11, clxsxviil. 

"Homo S(.(iU<! anit Dyniiiiiic! Kiulnmiira Tests," 
Int. Assoc. TenL Mat. S'rw., 1012, I'IIJIIT V. 

' MiiHchpHtor Kteani llHora' Anssiw., aicsmo, by tllilrf 
IJiiKliH'or, 1IH3. 

" " li'ntlBue Jlciullng TcslR," A'ci'cncf j'l&simcfs, HIM, 
No. 1371. 



In 11)02 Owlinnut 

.Hoysiolds and J. II. SmiLli 1Q (li'sc-ribud n Uinnv 
tfistitig mftcliine, for rovomulu (if ulri'Hrt in 
wliioh diinnlo dircsot HtroHHrs \voro pniiliKti^l nil 
atcHlipit!i!o!y tbo iinniin forcscsof nmipnioiLMn^ 
weigh CH driven liy u isruiik und runiu'-dtiiif; rod 
from a volating sliafL. 

A mtuihiiio of HID Hainn tyjio \vtin tli'sij.(ni'd 
by T. E.Stanlon 3 " and UBCI! for fiiji wult <ui (1m 
of iron and nii;nl tn rnvernalH of 
A ditignini <if tho intn.!liaiiiHni. 



" ii.(!int!ili!il Htri!KHr!," Qttartrrlti Junritiil "f 
Ulintsrtcjtmt-'tttt fitsl. uf Trrlutalatift, 1HI1U. 

lu liiiiihwcrliiK :U)!(!(inl, Hisot. aa, LUDft; ulHii fiitrr, 
AKSOO. 7V;s(. M'tl. I'rw,, 11100. 

11 rtifl, jl/crft. Knu, Woo., r<t., IH-d. lilll. 

" ItoU. San, Pltil. Trnnti. A, 11)02, cxdx. 

1J Jfitgiiieerinff, l>'cb. 17, 100D. 



182 



ELASTIC CONSTANTS 



isi wbown in .Fig. 105, which also explains the 
method of ImlniKsing Mio cranks. 

lAmr imisHRH M reciprocating horizontally 
arc operated by four crunks C. There arc 
therefore- two independently perfectly balanced 
systems with cranks sot ISO" apart on tho 
aamo sJmft All. The cranks of one. system 
nro at riyhl imglcs to the cranks of the other 
Hystoni, BO Unit tho lunotiu energy of the 
moving parts ia thus approximately constant. 
There mo four test pieces S, one stressed by 
each rowm'doating ninns. 

Machines of thU typo, however, suffer 
from llio disadvantage that the inertia fnrcos 



end to the frame of the mathirio in 
way that its height can bo adjusted to 
for elongation, while the lower end is 
to a frame carrying tlio armature -A- 
two-phase electromagnet M 1 and M a . 

Tlio eleelfomagnet is excited by an 
ing current from a generator giving 
wave E.M.I 1 '., KO that tlio pull in 
proportional to (voltage/frequency) 2 , 
independent of tlio air gap, which I 
and pulsates with twice the frequency 
electric current, 

Two small soooiidary coils ivound 01* 



* ll 



*"- Hltltl 



i ic^a i'l,V 
iiuill 



f I' 



are fixed close to the polo faces, and tlio vc>H 




FIG, 100. 



vary with tho atiunro of the upeed. It is 
thoroforo iiuooasary to control the speed very 
carofully if reliable reaulla arc expected. 

(iv.) .Direct Stress Machines. Load applied 
by piiEl of an electromagnet oxeUorl by an 
aitoniating cnrront. 

Thia niotUnd haa been auecessfully ajiplied 
by (I. Kapp, 1 15. HopkhiBon, 2 and B. 7?. Haigh. 3 

Jlaigli haa introduced several now features 
into Iiifi latest design. Fig. 10(i allows a 
machino installod at Llio N.P.L. and Fig. 107 
iHimtradsH tho principle atlopted. 

Tlio test IHOTO H in coiinccterl at ita upper 

1 " AltorimtliiH Kl-resn Machine," Zcils. V mines 
UcnlMh, Ing,, AUK. 2(1, 1011, 

1 Hoi/. 8<ic. J'roc. A, iltni, 31, 1(112, Ixxxvl. 

" Jlnaineeriiiff, Nov.sa, 1012; aleo /*(. q/A/ctefe J., 
1017, So, 2, p. 56. 



ll- 



indnced in those coils is measured by H, 
meter ivnd used for calculating tho sti'oaa. 

In order that tho pull of tho two 1 111.1 fi] oin 
shall bo of tho sumo amount it is iiouoHHiiry 
that tho air gaps shall bo equal. A Umi 
adjustment ia provided with tho nmeliiiici [n 
enable the test-piece frame and anmit.urft in 
bo raised or lowered during a test uitt.il tlui 
onrront in tho two coila and bhorofoi-o thn 
air gajia are equal. The coils arc ccjmT~io<itu<l 
to a flillorcntial ammeter which read** Kcini 
when this condition is fulfilled. 

By the use of a choking coil tho voll-nj^n 
readings are rendered nearly indoporitloiit of 
tho frequency over a fairly largo rotngo, tm 
that slight alterations of frequency during a 
teat do not alter the range of stress. 



ELASTIC CONSTANTS 



183 



Tho frame carrying tho test piece mid 
armature is also attached, below tlio latter, 




107. 



to standard springs S, S. Tlio stiffness of these 
springs is adjusted to counterbalance tlio in- 
ertia of the armature, etc., a precaution which 
18 very desirable, aa it eliminates a correction 
which would amount to 5 per cent of tlio stress 
range. This adjustment is ofl'oeted by-sotting 
the springs, BO that the moving system, 
without the teat piece in place), vibrates in 
resonance wilh tlio magnetic pull. 

By extending or compressing the springs 
an initial pull or push can bo applied to the 
test piece so as to alter tho magnitude of the 
minimum stress, 

Thus if /(, = tho alternating stress applied 

elcctromagnelically, 

and / = tho stress applied by tho springs, 
then tho maximum stress (f uiaf .)=fe+ft 
and tho minimum stress (/,,,in.) = ~fa+fr 
Range of stress = Z =/. -fann,=fe +f+/a~fs 

-2/d 

i.e. tho range is not affected by the load 
applied by tho springs. 

Tho voltmeter is calibrated by measuring 
tho range of stress (photographically) by a 
special form of optical oxtonuomoter. This is 
shown diagrammatieally in Fig. 108. 

(72) BUTKOT OS Sl'KBU ON THE LtMITIHa 

RANCUB oi' STHHSS. Reynolds and Smith 1 
found that tho limiting range of stress was 
smaller at speeds of 1300 to SfiOO per minnto 
than at 00 to 80 cycles per minute. Their 
conclusions havo not, however, been confirmed 
by subsequent experiments. 

Stanton and Bairstow, 2 using a machine 

1 lion. Sac, Phil. Trans, A, 1002, cxolx. 
a " Healslfliico of Iron and Steel to Reversals of 
Direct Streaa," hist. Civ. Eng. 1'roc. clxvl, 78. 



of (.lie same type, found that n change (if 
speed from (10 to 801) did not sorioiiBly 
affect tho range, and later, using a machine 
of tho same typo as Wohler, they found 
that there was no evidence at all of any 
reduction in fatigue strength duo to a mfo 
of alternations of 2200 when compared with 
200. 

With respect to Reynolds and Smith's results 
Stanton snys, "It seems probable that the 
reduction in fatigue strength noted by 
Reynolds and Smith aa duo to high rate of 
alternations is a characteristic of the particular 
mechanism used for their experiments." 
Bairatow 3 says, " It may possibly be that the 
decreased range of stress found by Reynolds 
and Smith has some relation to tho question 
of recovery, but further experiments are 



Mirror attaeliail to T#si Piece by two 
Springs (t), gluing a. virtual centre of 
rotation on the axis of Uio Tost Piaca 





-Tost Pleco 




Via. 108. 

necessary to decide tho question, as tho ofl'eot 
of tho rigidity of the testing machine IHIH not 
yet been fully investigated. In two instaneCH, 
at least, low ranges of stress have boon traced 
to natural periods of vibration in the testing 
machine agreeing approximately with tho 
period of repetition." 

Eden, Rose, and Cunningham * found no 
speed effect between 2CO and 1300 revolutions 
per minute. 

" no;;. SOB. 1'Jiil. Trims. Scrlra A, cox. nn-!i5, 
1 Insl, Mcch. ling. JVoe., Oct., Doii. 1011. 



184 



ELASTIC CONSTANTS 



g (7:t) Ki'FK 

AND HuiU''A<;]i OoNllLTlON OK TI1H .LliMITlNCI 

KjUNOKS or STIIUSS. Stan ton and llmnitow 
have sli\vn (hut rapid (shangtsu o 
a marlioi! cllcct on tlifi riifiistaiusD of materials 
to repeated direct stresses. 
The standard lost piece that they mod had 



depend on tho ImrdncHs of tho fd;rol iH'intf 
approximately 52 per cent for tlio liiv* 1 "* .Hindu 
and 4fi In .'55 per cent for tho wroni?' 1 *' i' 1 '")- 1 ' 
and mild stoeln. 'It is, however, worl-lt.V '^ 
notice that even inn lor tho eircu in *('* nr j (111 
supposed to be inoBt fatal to hnM atc^'sln, i.f. 
a midden change of section, thcso . 



Jlntcrliil. 


1'oraifitiififiJtcdiid.loji of t.lie .Liniitins Jinnsft of Sh't'ss^. 


Hl>n<!lniBii Si-row cut 
with 11 VnnThiViul. 


S])('(!l)Hcii IiaviiiR n 
.VilUit 0-OOa in, Jtuiliim 


KiH-.'immi !'>>"< ^' 1M| 


>S WGd tall JIl'.HSUIlK'l'Hll'ol Nil. .'! 

Kwcdinli He.sHt'mcr iilci-l Mo. 2 


SI 

;to 


32 


G2 


tSwc-disli Jicsst'mi't- sti'i-1 No. 1 


33 


32 


fi2 


iSwnltah ulumittiil iron 
J'isliui-i'od Kiwi .... 
IMiM Hti-cl No. a .... 
UliliUlni.'! No. 1 .... 
Wrought iron Mo. 1 ... 


32 
33 

29 
20 
2,1 


35 
20 
28 
28 
10 


Ifi 
40 
4B 
36 

40 



a fillet of ;J inoh, and for eompariHon with 
tliia thoy made oxpcji'imenta when (!) tin; 
fillet \vii9 roduoecl to ()-Oli2 itiuli, (2) the 
B|)(!imcn wna Hnrow cut with a Whitworth 
veo thrend, nml (li) tho corners wore loft 
sharp. 

The results are givon in Table- 20 and 
show 

(1) That tho resistance of all theso fnnris 
are, in every easo, far Jiulo\v tho COITC- 
8[ioniling maximum Huiithig resislaiiees iE 
tho materials, 

(2) That tho resistnnec of forms (1) and (2) 
are practically UIOHIHIIO for any ^iven inateriul. 



veiy appreciably stronger than wrwi 
and mild stools. 

The results of some cxporimontH, 
tho author HfmiH tho Wiihler rotating 
vnoUmd of tout, are given in Table 
.standard test pieuo sliowii in Jt'i/j. lOil 
radius' of ()'(2fi ineh. 

The percontago redncLion in the iv 
seen to agree with the results obtiLi m 
iStantcin and Biiii-stow. 

Tho injurious cflcet of fieratishos in 
machinery aiibjoot to variations of 
now recognised. ITaigh says that 
develop from fiiirfaoo Bcratehes uncUjr 



HO, 



j 



hn 
H a 




fllaterliil. 


Dlt-iiiiad! HiuUc 

!L'onn pi;r 
8(], In. 


Limit 

a 

Klllot 

Sin. itiiiiins, 


7ij{ Kaiuto of Ktrossi. 
OHM in-r KH. In. 


SFfi?;! tin 

I.NSL" l(Hl!| 


itaffiL. 


Sharp 


Ninkfl olii'dino uliutt No. 1 


01-0 


C7-0* 


48-0 


ai-o 


4U 


.Nickel (ilirtiinii wliufli No. 2 


Jfi-2 


dO'O 


.. 


2D-4 


a 


Hoilfir PIulo .... 


27-0 


27-11 




1G-0 


^s 



* 57-0=>-|-28-C to -28-fi, 



rind tliat tlio ratio of tlioao resistiinecs to tho 
ug inasiininn limiting rcHistancea 
not vary giwiLly for the different 



(;i) That in tho ea.so of tho Hpotiimens having 
n, siuldon clifinge of WHition, tlio pisi'centago 
reduction of tho limiting range appears to 



perceptibly lower than tho normal. J'n HI mm 
experiments earned out by tho autlmi- [.hiv 
altornnto stress range of BOHIO aoro oraiik- 
shaffc inatorial wan reduced from fifl-0 ( -j- ^9 (<> 
-28) to 49-0 tons/aq. in. by a Bhurij HoruLcih 
0-003 in. deep. 
TJiei-o seems to bo no doubt that iimny 



ELASTIC CONSTANTS 



ISfi 



fatigue failures uttribuloil I o faulty material arc 
really due ID unsuitable (illots, Hliai'j) earners, 
or surface scratches left during the process of 
machining, 

{74) .kliSIttTANOB OF MA'I'MliUr^ TO C'oM- 
HiN !: u ST n tosssMH. Jfrornicnt CJIHOH of tho 
combination of stresses are mot with in 
engineering practice, and tho question of tlio 
resistance (if materials to those stresses is 
mm' recognised as being of considerable 
importance. 

Htrcss applications may bo til three types : 

(i.) Simple stress or dtrcsa in one direction. 

(ii.) liiaxial stress or two stresses acting in 
directions nt right nnglcs to each other in tho 
Bdino piano. 

(iii,) Triaxial (.trows or tho application of three 
s tresses at right angles to each other. 

With simple stresses, direct tension or 
compression, tho practical constants (modulus 
of elasticity, clastic limit, yield stress, iiltiinato 
stress, Poiason'a ratio) uro taken as a basis for 
design, With complex stress distribution tho 
(juestion arises as to tho way in which thcso 
constants nro to bo used, and several din'erent 
theories have been expounded to account for 
the method of failure of materials nuclei' 
coinbinaUons of Htfoswi!. 

Tlio more ini[)iniant raws of compound 
stress, considered from an engineering stand- 
point, are liiaxiul. 

Shear in an example of biaxial (dress bcuiniKo 
it is {;([iiivalcnt to the combination of two 
equal principal sti'esHcs, 1 nno compression and 
the other tension, acting in directions at 4fi 
with tlio fihearing fstress. Tluw, in Fig, 100, 





]fl(J, 10U. 

tho stress on the piano A'B, at right angles 
to tho axis, is pure aheiir, tho intensity of 
which dop on da upon tho diameter of tho bar 
and tho tonjuo applied. This shear is a, 
combination of tension nlong tho 45 pknci 
01) and compression along tho plnno EF, 
It is well known that mild steel and wrought 
iron fracture, in a torsion test, across tho 
piano AR, Le. a shearing failure, n'hilo eusfc 
iron breaks along tho plane I!F (i.e. faila in 
tension) because it is stronger in shear than 
m tension, 

Other combinations of biaxial stress are : 
() The crank - Bhittt -which is beat nml 
twisted at the samo iimo. This can bo 

1 Sco "Elasticity, 1'licory of," (5). 



reduced to a onsfs of trnainn cmubiiH-d vvitli 
eomprcssion owing tu tho f.(]i'i|iie j)rnchic:ing 
tension and ('imi)ire.sNioii on two plunc-a til 
right angles as dcsciibed abovo. 

(b) [['be shell of a aUifiin boiler, which lias 
to resist cirisiniiferential and hiiigitiidiiml 
stresses, is an example of tho coiubiimtion of 
two tensions. 

(c) PJtilcs, concrete slabs or floors sup- 
ported round the edges iincl louded in tin: 
centre, are fiiiihet 1 exuinples of Ijiiixinl wlt'cas 
distribution. 

TJirce-dimensional stress in fduiul in thiok 
steel cylinders under internal pleasure neconi- 
paniecl by a Jdngitudinal toiiiiinn, nl.sn in 
concroto colinnns with spiral leinf.inicnmnts, 
and in bdoped guns. 

g (75) CAUSUS OF FAii.tnti'! IN COMIIINI:D 
KTIUSSS. Investigators in the " eoiiibined 
stress" Jielcl of rcscnrch Inivo firsl of all lo 
decide upon whnt thoy cotiHider tho point of 
failure- i if ft material. The elastic- tbeoiy, 
being bawd on lidoho's law, is reliable, up lo 
tho clastic limit (limit of proportionality or J 1 
limit), and thort'fore, consiclered inntbeniatic- 
ully, tlio ckstiu limit is Hie jinint of failnrn. 
Thia liniid is (lci|iend('iit on the prtwimm 
history "f the matorial, mtd in thoroforo 
varfa.l>li) and indefinite. For oxpi-riiiK'ntiil 
piirjioses Ibc yield point IK tiBcd, in a yiind 
many instsini:t'H, as the, ciltcrinn of failurt) ; 
tin's is no doubt due to the, method of hinting 
which does nut nllow the tests Lo lie continued 
to the point of fjiiluro. 

'I'lie must iinjuitlHiil t!n?iuieH iidvnnced In 
account for tho failure of material under 
combined stresacti uro : 

(i.) M(t-j:intiii til>-ct,it Theory (Hiuikiim), 
This theory is that the inahsrinl yidld.s wliOTi 
ono of tho principal B(resH(ja reaches n oerlftin 
imioinit. ('I'lio stress dottsi'inincd by a eiitipln 
tenmlo tost.) It tissiuncB that a second stft'HH, 
at right anylc-s to the first, neither weakens nor 
Hti'ongthens tho oviginnl stress. 

(ti.j Maximum Strain Tfienry (tit. Votiant). 
liy this theory faihiro i asBumod to ocenr 
when tho inoiimim strain reaches a, vnluo 
equal in inagnitiidc to Hint at the yield point 
stress of tho simple, tension or coinprcKsion 
ox]ioriniont. 

If a material ia subjeotod to two or tlireu 
stresses at right, angles to each other, iho 
inaximmn strain theory ussiinu-a that' tbn 
strength is lowered if the BtivKseii urn (ippnHite 
in sign and increased if tboy arc of tho 

sign- 
Thus if tS p S fl , and S s nro three 
riglit anglea t<i rach other, nnd e lt e., t and e :i 
arc tho unit strains in tho dircutii.ni of oiuli 
oE tho respectrvo stmsacs, also 

]5=the moiluluH of elasticity 

to be cnnattmt) 
and l/u=Poia3on 1 fl ratio ; 



186 



ELASTIC CONSTANTS 



then 



For simple tension S 2 and S 3 may bo taken aa 
aoro ami 

p _q p^^i^-^i!^ 
i H, . '~ p^ strain* 

which ia tho expression of tho modulus of 
elasticity. 

The maximum strain theory is mathomatic- 
nlly correct if it is assumed 

(re) to hold within the clastic limit, 
(i) that liooko's law in absolutely correct, 
(c) that the material is iso tropic. 
((/) that tho effect of temperature is 
negligible-. 

By taking tho yield point as tho criterion 
of failuro, the variation of " 1C" between tho 
limit of proportionality and tho yield point is 
assumed to bo without oft'cot on the results. 

(iii.) Maximum Shear Theory. This theory 
assumes that tho condition for initial yielding 
of n uniform ductile, material corresponds to 
tho existence) of a specific shearing stress, the 
intermediate principal stress being without 
effect. 

This theory as originally proposed, by 
Coulomb in 1770, refers to rupture of 
tho material. It is adopted in Guest's * 
well-known work (1000) whore it is used in 
conjunction with the yield stress. It ia 
approximately verified by W. Scoblo a and 
W. Mason. 3 

Wo can assume that simple tension is a case 
of combined triaxial stresses where two of tho 
principal stresses are zero. Applying Guest's 
law, the bar must fail in shear, and in thia 
case tlie maximum shear occurs in a piano afi 
45, and tho shear stress intensity 18 fiO per 
cent of tho tensile unit stress. Sooly and 
Putnam '* find that the correct ratio of nlastio 
shearing strength to tho olastio tensile strength 
is 0-55 to 0-06, and therefore state that Guest's 
law which assumes tho value to bo 0-f5 is nob 
a correct statement of tho law of elastic 
breakdown. Booker 6 found this ratio to 

1 " StroiiRthof Materials under Combined StreHSca, 1 ' 
I'ltit. Mag., July 1000; and Plii/s. Soo. Proa,, 1800- 
1001, xvlf. 202. 

* Strength and Behaviour of Ductile Materials 
tinder Combined Stress," Phil. Mail., Dec. 1000, 
-Xll. B33. 

1 " Mild Steal Tubes in Compress Ion and under 
C'nmliiinKl Straw," lust. Mee/i. Eng. Pros., 1000, 
Hurt iv. 

1 Uiiii'iirait// of Illinois Jlullelin, No. 115, Nov. 10, 
1010. 

6 "Tho Slroiifflh find Stiffness of Steel under 
Blnxlnl LondhiR," University of Illinois bulletin. Wo. 
85. April 10, 1010, 



IKI 0-fifi, and tho author a obtained 

of 0-03 to 0-(i8 for steels Avith ultiiin'f" 

strengths of 2,'i and 30 tons por iu' *'" ill< '' 1 



.Becker, 7 as tho result of oxpoi-imon 
proposes two laws of strength mulur c 
stress, viz. : 

(1) That the strength nt tho yic-lel inl. 
follows the Maximum fit rain theory niiii' llm 
shearing stress reaches tho vtiluo of' tlit* Hln-ur- 
ing yield point. 

(2) After this point failure- oecuva n.*-<* l ' ( ''"'' 
to tho Jlfaximum Shear Theory. 

Thin sugyoatioii appears to fit in vorjy ivi'll 
with existing oxpcriiuental "work. 

The maximum shear strews theory luif" l'i'H 
modified by Puny to include a .fniitii >iiu I torm 
proportional to tho stress and porpoiifl iisulnr 
to tho piano of sliear. Ho nuticc-s* I Mini, 
brittle mate-rials fracture at uindoM ^rcii^-r 
than 45 with tho ci'oKs-sctition ami iii-i^iinn'ii 
that thia is duo to internal friction. 

If = tho angle found cxpm'iiii^ii'-fi.lly, 
j). (tho coefficient of friction) = lai \\ 'j'i 
then tf='l!)-|-^/2 for tension and Q~~'\ f" -- </'/" 
for compression. 

.For oast iron tho angle (0) ia foiiod tt> I" 1 
5'iJ , which gives ii value of /j, of 0-3/i. 

If </> = 0, this theory is tho sanio n llni 
nmxiniinn shear thc-oiy, and Perry wu.j.fj-^:^!! 
that this ia the cano for wrought jroii ninE 
mild steel. 

(iv.) The Maximum lieniltence %' fif-of */.- 
Haigli c proposes that tho elnstio limit <jf IL 
materiiil under complex stress is rencfh<M-l \%'!HIII 
the energy per unit volume attains iv tsoi L-Jiin 
dofinito value. Ho bases this view on t-ln*riiio- 
dynamic considerations, and also fiu*!** tlinl, 
when eonsidorod from tho uxporimenlitl tif-t|M-<'l, 
tho rosults fit in with this theory Iu*Mi'i f 
than they do with either tho nuix j 
stress, maxinuim strain, or maximum 
theories. 

Mallock considers tho voluino o^cl 
limit or tho limit of shear as the fniiitj.i,iin'ntul 
limits of a material, and assumes) (1ml;. ilm 
material iviil fail when either limit hut* l>i-ivn 
reached. 

(7(1) EXI'BRIMRNTS OHCoMniHMntS'rilKHM.- 

Most experimental work lias been cnn-ior] *-ul, 
on ductile materials. Only a low o.v |nm- 
monts liavo been made with brittle inttifuridlFS 
find further research in this diraa t i* i i in 
needed. 
Teat on thin tubes in combined tcnmoji tui'\ 

* Batflon, Insl, Ulee/i, Stiff. Proc,, arari-lv J1HV, 
D< 182, 

'"Tho fttroiiRLli and Rtiffnosa of S(:<-r^l uiitii-r 
Itlnxinl LoitdinR," University of Illinois J.iutii-fit No 
85, April 10, 1010. 

8 " The Strnlii-l'jiicroy Function and tho 1'itjiKrin 
Limit," llepQrt of British Association, liJMJ, Jim | 
Engineering, Jan. 30, 1020. 

8 lion. Sac. I'roc. A, 1000, Ixxxil, 20-*>1>. 
Dec. 1012, u. 40U. * 



ELASTIC CONSTANTS 



187 



torsion have been curried out by Guest, 1 
Hancock, 3 Turner, 3 Mason, 1 ' and Becker. 5 

Hancock and Turner used the limit of pro- 
portionality UH the point of breakdown, Guest 
and Mason took the yield point, while Becker 
adopted the " apparent " elastic limit. This 
is a point between the limit of proportionality 
and tho yield point whore- the slope of tlio 
tangent to tho stress-strain curve is 60 per 
cent greater than it is at tho origin. Seely 
and Putnam G also used tho " apparent " elastic 
limit in their experiments. 

Guest, Turner, and .Becker added internal 
fluid pressure- in order to obtain an additional 
stress. 

Solid round specimens under tension or 
compression and torsion have boon used by 
Hancock, Scoblc, ' and Smith, 8 while tho 
strength of thick cylinders under internal 
pressuro has been determined by Tumor, 
Cook and Robertson, 10 and Brklgeman. 11 

Crawford ia used Hat steel platea clamped at 
tho edges and subjected to fluid pressuro on 
one side. 

(77) REPEATED APPLICATIONS OF COMMHED 
STRESSES. With repeated stress tests the 
limiting range of stress in fatigue is n value 
that can bo definitely taken us tho one at 
which the material fails. 

Although \Vohlor made tests under repeated 
tension and repeated torsion, his results are 
difficult to compare owing to lack of specific 
information regarding tho material used in 
tho teats, 

Both Turner and Stmmoyer 13 have experi- 
mented with alternating torsion } tho formoi' 
found that the more ductile materials approxi- 
mated to tho maximum shear stress law, while 
tho moro brittle samples were more nearly in 
agreement with tho maximum utraiu. theory. 

1 "Strenglli of Materials under Combined Stresses," 
Phil. Mai!., July 1000; nml Pltys. Sac. Proc., 1800- 
U)(U, xvll. 202, 

! IS ng. NCIVK, Auc. 2-1, lOOfi, Hv., and Sept. 2, 
1009, Ixll., und Phil. Man,, Out. 1000, Fob. 1008, 
niul Nov. 1008. , , , nn 

3 Engineering, Fob. 1000, Ixxxvil., mill July 28, 
1011. 

1 " Mild SUsel Tillies 111 Compression and under 
Combined Stress," /(, Mfdi. Xng. Proc., 1001), 
part Iv. 

I " Tho fitrciifitli nud Stiffness of Steel under 
Eluxliil Loaillng," University of Illinois Jhtlktlu, 
Mo. 85, April 10, 101 0. 

University of Illinois Bulletin, No. 116, Nov. 10, 

' " Strength and lloluivlnur of Ductile Materials 
under Combined Stress," Phil, Mag., 3>cc. W. 

' Engineering, Aug. 20, 1000, Ixxxvill.; Insl.Mefh. 
Enti. Vrac., WOO, part Iv. ; Inst, of Metals, fourn., 1000 ; 
Iron and Ntcel Inst. Journ,, 1010. 

Engineering, Fob. 1000, Ixxxvlt., and July 28, 

10 '" The Strength of Thick Hollow Cylinders under 
Internal Pressure," Engineering, Dec. 15, 1011, 
xcll. 

II Phil. May., Jan. nml July 1012. 

13 Ron. Nor.. Edinburgh Proti., 10I.1-1012, 
13 Manchester Steam Users' Auaoe., Mom. by 
Chief Engineer for tho year 1013, 



The only experiments so fur carried out on 
combined torsion and bending were those by 
Stun ton and Unison. 1 ' 1 A diagrammatic sketch 
of the arrangement which was adopted is 
given in 7<'ij/, 110. In the position shown the 
cross-section of tho specimen at S is subject 
to a twisting moment WD, nml to a lending 
moment Wrf. When the head hurt turned 
through 1RO the moments were equal in 
amount but opposite in sign. When tho head 
had turned through tl() from tho position 
Bhown tho maximum stress was that due to a 
Lending moment W.f> plus thai due to tho 
direct loading, but as in all cases this strews 
wns below tho known fatigue limit of the 
material under reversals of simple bending, 
ita effect was taken to bo negligible, and 
tho specimen was assumed to be subject to 




''id. 111). 



reversals of tho combination of bending and 
twisting alone. 

(78) Ar.TEHNATINO BKN1HMI TKSTS IIHYOHI) 
TKii YIJ<;LD POINT. Tho principal objection 
to tho commercial adoption of repealed strips 
tests is the time and expense of conducting 
tests in which millions of applications of stress 
are required in order to obtain the result. 

Many machines havo been designed in which 
tho test piece is broken rapidly under alter- 
nating stresses which exceed tho yield point. 
Suoli tests do not give information as to relative 
" fatigue " strength of materials, but huvo 
been found useful as indicating mechanical 
defects, incorrect heat treatment, and brittlo- 
ness. 

(i.) ArnoldTeslingMacMna. 1 * In this test, in 
its latest form, a teat piece |- in. diameter and 
C to in. long is firmly lixetl at one end 
in a vertical position in tho vice of tho machine. 
It is bont backward and forward, through a 
distance of jj in, on either side of the vertical 
at a height of 3 in. above tho face of 
tho dies, by a blotted steel head lixeil to tho 
reciprocating part of tho machine. Tho 
length of slot ia larger than .tho diameter of 
tho test piece (usually -J in. with a stroke of tho 
machine of 1 J in.), so that an impact or shook 
is introduced at each alternation of stress, 
Tho standard speed adopted is fifiO alternations 

" Itejtarto/lhcJiritishAssoeiation, Newcastle, 101(1. 
' " lectors of Kufoty In Mnrlno Ki 
Engineering, 1008, Ixxxv. COS, 



188 



ELASTIC CONSTANTS 



per miniile. The number of alternations to 
fracture is recorded, Arnold jind other inves- 
tigators improvised shaping or Hlottiug 
machines to perform tho le.sl, 

It should be noted that, in !iis curlier work, 
Arnold l used a test piece jj- in. stjiifirc. with 
the force applied 4 in. above ilio lino of 
maximum stresH. Tlio deflection was | in. 
or -ft in. OH cither side of tho vortical, and 



Tcsi f fcco 



Too/ Steel Hammer Dlav 




tlie number of alternations was KtS to 2(i(i 
por niiniito. 

(ii.) Landyraf -Turner AUermiing Jinpnct 
Machine. This machine is especially designed 
and constructed to wiry out tlio Arnold test in 
order to standardise the contlitions employed. 
In place of the straight line movement of tlin 
shaping machine a rocker arm is substituted 
(tfiff, 111} to economise spueo and, by reason 
of its radius being equal to the freo length of 
the lest piece, maintain a constant leverage 
during the wliolo stroko. 

Tlio number of alternations are recorded by 
a veedor counter which stops registering when 
tlio tent jiieiio breaks. The test piece is $ in. 
diamotor, but, with this machine, the distance 
from the top of the vice to the .striking point 
of tlio hammer is 4 in. instead of 3 in. 
aa used by Arnold in. his latest experiments. 

This machine is miumfnoturcd in tlio U.S.A. 
by Queen & Co., Philadelphia, 

J. _ B. Kommers a of the University of Wis- 
consin has carried out an investigation with 
a Landgraf- Turner machine. Ho summarises 
his results as follows : 

(a) A very important factor in a repeated 
Ktrcsa test similar to that performed by the 
J/amlgraf -Tumor machine is the amount of 
deflection ivliioli the specimen receives. When 



(Hiipjilomonl), mos, and 




the defleotioim are ICKH than O'liO in. tbo 
ebange in the number of cycles requireil for 
rupture is very great, oven for small changes in 
the amount of ddlcction. 

(it) Impact applied to the specimen hua 
pnifliaillif no effect upon the number of cycles 
required for rupture. 

(c) At s]iced.4 of about 700 cycles per minuto 
tlio number of isycliis for niptnro is slightly 
less than at speeds of about lot), but for small 
changes of speed this effect in pracl.ieally 
negligible. Wbcn tiio dofluistion in small tli'n 
results oil the same inaterial do not seem to 
bo as uniform as when tlio deflection is about 
();!() in, or more. 

((/) The condition of the surface of the spoci- 
men has mi important effect upon the number 
of cycles required for ntptiim. 

(iii.) ti<inl.-e>i Itiind Jiemliii!/ '/'e,s(. B Tliopriii- 
ciplc on which the lest is based is to bend back- 
wards ami forwards a lest piece jj in. diamotw 
and 4 in. long through H fixed angle until 
failure, tins numbi.'i 1 of hc.nds and enei'gy 
required For wicli betul boing recorded. Tlio 
tewt is etirried out on 11 nmehino, maimfac. 
lured by (.'. \<\ Casnlhi ft, Co., J.td., and shown 
diagi'ammatically in ./'';';/. 1 1 2. A flat slwil 
Hjiring ]i has ono end gripjied in a vice A 

O H 




which forma part of the bedplate, and tho 
other sccuvod to a bolder in which (lie IcsL 
piece .1) is fixed. Tho test piece is also held 
in a handle 1C, 3 feet long, by which it is Irani; 
backwards and forwards through nn angle of 
01 D located by the indicators ir and ]<'. 

The energy required to bend the tost pieeo 
is measured by the deflection of the spring !li, 
which ia recorded on the paper allachod to 
the drum G. The horizontal motion of tho 
pencil H is actuated by tho holder 
through wires L and M and tho multiplying 

l<:>iaiit?frintr, Vc\>. 15, ]j)07, p. 200. Dec. 20. 1007, 
p. 820, ami Doe. 27, 11)07, n. 882. 



ELASTIC CONSTANTS 






* * J ufc this IH Hmnotimoa replaced by ;i 
J'liiying from the wire M which then 
<>Vor u vertical pulley. Th<i motion 
i^OtiC'.il i.i propoHmnal tti the energy 
"til beml tho lest piece. Tho diagram 
*M;eil by noting tho length which eorre- 
, ** n measured pull at a known leverage 
*-* point of bonding of tho tosfc piece. 
uent of the pencil Imldoi 1 H moves 
"-i-l,* 1 " 1 through DUO tootli of a ratchet 
* "which is attached to if; HO that a 
, * in drawn ancli as 19 shown on tlio 
ll *- thn illustration. 

x(.i(.ical vulno of tho Snnkoy lest is 
Hath'old, 1 who curried out an oxten- 
with it, to bo IIH follows : 
10 energy absorbed in breaking tko 
y t>8t pioco is praelieally proportional 
J.*i'* icliiet of tho average bonding moment 
lt * number oE bunds withstood. Those 
may bo compared roughly to tho 
Btrcsa and ] i ednctio]i of area in tho 
fc, i.e. for conditions of increasing 
in ,goneral, tho maximum bimding 
iiiercaaDS and tho number of bends 
. It if) noccsHiiry that wo should 
tliat in a number of instnucca wo 
>l>l-jvincd high iibnorptionH oE energy with 



^o inaxiin\un landing moiuout in tko 
y tt?rtt follows tho maximum strew in 
11 JFiiirly closoly, so that tho latter values 
i ~li'oilieted within a few tons per MCIUIU-O 
i-'oiiL tho Siinkoy values. Tho variation 

*i tho vnltiOH of tho jiumbor i>l bonds 

H*uilcoy lire rather wider and of a leas 
t-fi.1 jlo nature. In thin ]'on])oot tho Saiikoy 
. i (scsi'i minatoa and omphaaisea a certain 
y c-*f tho material in a manner not 
\'ly Ijroughl; out ia other teats, except 
>f* tn.i fiomo oxlont in tho Arnold test. 
it lciowlodgo of the quality of tlio stool, 
n.lj.'titH, etc,, expoiieneo baa shown that 
tlofinito values of ductility in the tensile 
FI in cuiHurcd, for oxamplo, by tho reduction 
n., f,nn bo expected in conjunction with 
A^fi.lnoa of tensile strenglh if tho Htoel JH 
L-oiii. tlofeotti. Similarly tho number of 

irt tho tSunlcoy teat Hhonid reach such 
i Avliitm witii ox])orioneo of tho test may 
jo fuii'Iy definitely established. Thcro 
rj \vovor, Kovenil outatandiug oxceptions. 
tti-iiily a[>|ii i am tliat samples, which gave 
y vitlucs well below what lias been pro- 

f i-oJii an avorago good steel of tho name 
> strength, wore in nearly all oases also 
,-litvfc inferior in reduollon of area." 

of tho Sanltey test piece ia 
its fi-co length 1J in. Owing 
ft\cb that tho machine, as supplied, is 

nnil 'Duncan, ff.li. Const Tnsl, of Jiiiy. 
'roc., March 10, 1020, 



not sniliililo for steels of liiglier toiiHilo, atreiiglli 
thfui nO to 00 tons per si|iiaro inch, Ihitfieltl 
suggeals a test jircce ()!! in. diameter and 
free length 1? in, fur tlie.so slock 

Siuikey a gives the following citustjints for 
infoi-ring static lest results from thoso (ihluinetl 
on his hand bending niaom'no : 

Yield point (tons per fit], in.) 

_ initial handing effort in His, -ft 

_ _,_ ..... ^_____ -, 

wkei'o G--2-1 for stecslrf up In O'l! per cent 
carbon and i2'7 for medium earhou 
steel. 

Ultimate strength (tons por. sq. in.) 

maximum bending effort in lhs.-fl, 

== ~ ........ ................... l-'fi-li 

I'llnnjration (on gauge length 4 s'Aroa) x 
reduction of ami 

number of bends 

" ........... I'-i) ' 



(iv.) The Ujiloit Lcmin 3 ttiHr/htipJiS tuxling 
mttrJiinp,, manufaelurnd by Thiius (linen T,osling 
Abiohino Co. (lOiiLrlish agent, Hdward 0. 
Herbert, Ltd., jUanehosiei 1 ) is very similar in 
jiriuciple to tho SanUoy iiimskine. It IH, 
liowever, ojicrated by a motor or boll.-drivo 
giving ii^O idtei'iiatioiiH per ininuto instead 




i-'m. 



of by hand, and tho method of measuring 
and recording the energy absorbed is slightly 
different, lioforring to Fin. H3i where tlio 
machino is shown diagrammatieally, tho tent 
]iieco is bent backwards and forwards by 
nn arm operated from tho adjustable crank M, 
Tho energy is measured by the amount of 
tho compression of tho springs El* 1 , which if! 

" Hanltcy, Blinnib, inul Klrlttilily, Tnxl. Mcr/i. ling. 
PtiM\, Mny JD10. 
3 American Muchiitislt Oct. 17, TJlii. 



190 



ELASTIC CONSTANTS 



recorded by tho bell-crunk indicator G marking 
on a continuous recording paper H. Tho 
form of diagram is shown in Fig. 1I3A. 




FIG. 113A. 

(v.) Oilier Investigators and Machines. Bou- 
douard ' used a machine in which one orul of 
the specimen was clamped in a. vice and tho 
free end vibrated. The vibrations wore main- 
tained clectromagnoticnlly, and tho oscillations 
were recorded optically and photographically. 
Sehuehart 3 tested wire under repeated bend- 
ing. Tho wire was gripped in (uirved-facod 
jaws and bont backwards and forwards into 
contact with the curved faces. 

Huntingdon 3 applied alternate bending by 
means uf an attachment to a shaping machine, 
(79) I-IAKDNKSS AND AmiAsroN TESTS. An 
examination of tho methods employed in hard- 
ness testing shows Unit onoli of them falls into 
one or other of two distinct categories. These 
arc : 

(i.) Indentation teals, in which tho surface 
of tho material under test is permanently 
distorted by the pressure of a hard Btcol 
ball, cone, or knife edge. 

(ii.) Abrasion or scratch tests, in which par- 
ticles of tlio material whoso " hardness " ia to 
bo determined are torn away from its surface 
by sliding contact with some other substance 
whoso corresponding resistance is so high that 
its surface romiuns unimpaired by the notion. 
If euoh of these methods were a measure 
of tho same definite property of tho material 
which Is as oimuaotoristio of it aa, say, its 
elasticity, it is evident that tho ratio of tho 
results of any two of the methods would bo 
the same for every material tested. Com- 
parisons between tho results of these various 
tests liavo formed tho subject of several 
researches which have been published (luring 
recent years. The general conclusions aa sum- 
marised by Tin-not' 4 appear to bo that, although 
an approximate agreement may seem to exist 
between the various methods when applied to 
tlio case of relatively pure metals in tlioir cast 
or normal state, yet when tho resistance to 
deformation is duo to tempering or to mechan- 
ical treatment no comparison is possible. 

That this should bo so would .seem to follow 
from tho consideration that tlio resistance 
which any so-called hardness is supposed to 

1 Jnl. Assoc. Test, AM. I'roc,, ]f)13, Paper V,, 

3 Slatd uiid Kiseu, .Tilly 1, IMS. 

1 last, of Metals ,/., lojfi. 

< " Hardness," Iron and Steel lust, J,, 1DOO. 



measure is that which tho body 
exerts against a complex distribution o 
over its surface which has partially <l<.-f 
or disinterated it and it i 



or disintegrated it, and it is evident 

value will dopencl, not on tlio stress e 

of the material such as its yield point, 

tensile and shear stresses, hut on intcjniK;<l 

stresses, tho precise nature and dmtriln 

of winch are unknown and whoso ratio ti> 

streaa constants may not bo the samo 

same method. If, therefore, such 

without qualification, bo defined ns 

noss of tho material in its broadest Htmrtc 

is clear that hardness is no more 

quality of a material than is tho str 

a piece of steel of definite dimensions. 

latter cnse, if the nature, amount, aii<l 

bution of tlio stress are known, its i-cw-siHtiiiinn 

1ms a definite value which can bo u*ilnulalc<l. 

The only difference between this casts tuicl Mint 

oUho hardness test is that, since in fclio cJuh'i-- 

mination of hardness thero ia no p*>HHiliiliC.,v 

of estimating the stress magnitude find (Jinl.i'i- 

bution, wo are driven more to diretifc h.-ior- 

vation of tho consequences of such diHt 

than to a cnloulation of these con HO 

from the known charaotoristics of tho 

Mechanical phenomena of this Iclncl nro 

familiar to engineers under other aspeot-H, HinOi 

as in tho case of the resistance of nltipH and 

aircraft to propulsion; but whereas iit Mit-mi 

latter cases tho problem is to determine llu< 

resultant force exerted by tho unknown prcwi- 

iire distribution, in tho present CJIHO, J*H in 

the corresponding one of tho resiat ivrmn cif 

materials to impact, tho unknown <|ini]i).y in 

tho ultimate resistance of the material l.i> Mm 

unknown stress distribution. In all tlio anw.'i, 

however, the practical method of solution in 

an oxporimontal one, and conaists cjf Hil1inj.{ 

up a similar, or nearly similar, stato of 

on a specimen of the material whoso Ij 

is under investigation, and noting its. . 

II. Lo Cliatelior says, "The problom thorn- 
Foro seems to bo to establish two 01- Llircn 
methods of reference for hardness, 
widely different results aa possible, 
imrdnoss (which is an essentially t 
phenomenon) may bo studied undoi* iUl lin 
[)liQHes. Afterwards, for each partionlivi.- itjh. 
plication tho reference method whicli ifi nuwt 
ap])licablo to tho conditions may be UHtnl." 

That this view ia now being aono|)ltul is 
indicated by tho development, in rccotit 
of what arc called wear teal's. Pat 
thero nro wear tests for monsuri ri f 
partieular form of disintegration whioli 
[>laco on the surface of steel rails duo to 
.oiling abrasion of heavily loaded wJi 
The characteristics of this kind of worir uro 
tho extremely small amount of tho roliUivo 
movement between rail and wheel {MKl I ho 
ligh intensity of tho comprcssivo BtrewH nfc 



HK 



((HI 



ELASTIC CONSTANTS 



101 



the lino of contact. On the other hand, there 
arc- wear teats of lubriciitcd surfaces in which 
tho pressure is relatively small mid tho rate of 
slipping large, anil tho same conditions of 
wear occur, without lubrication, with pins and 
cheek gauges. 

ij (80) INDENTATION TKSTS. Tho indentation 
method of determining hardness has been 
applied in three ways : 

(i.) Hy testing tho material with itself. 

(ii.) By pressing (statically) a harder material 
into the material utulor test. 

(iii.) l!y producing tho indentation by drop- 
ping a bull- or cone-pointed hammer on to tho 
material and measuring tho rebound of tho 
hammer or size of tho indentation. 

(i.) The AFitleritil tented with Itself, Reaumur 1 
in 1722 shaped right-angled prisms from two 
materials which ivcre to ho compared and 
pressed thorn together. The axes of tho prisms 
wore at 00, and tho right-angled edges oamo 
into contact, forming a cross. Tho relative 
hardness was measured by the depths of tlie 
indentations. 

A. Foeppl a used two cylindrical lest pieces 
of tho material whoso hardness was required. 
They wore placed one on tho uthor, with 
their axes at right angles, and wore pressed 
together in a testing machine. J?oeppl used 
tho pressure per unit of flattened surface as 
a measure of tho hardness, buenuso ho found 
that tho surface of indentation was propor- 
tional to tho pressure applied. 

Haigh 3 has recently re-introduced tho test 
with tho substitution of square for cylindrical 
or triangular prisms. Ho given tho hardness 
number as = L/.li a , 

where L = thc land 
and E = tlio long th of damaged edge of prism. 

Reaumur, J'ooppl, and Hnigh's methods are 
shown diagrammatically in Pig, 114. 

Tho necessity for tho uso of two teat pieces 
is probably tho reason why this method of 
teat is not commonly applied. There is, 
however, no limit to tho hardness of tho 
material which can ho tested, as tho test is 
independent of tho use of a harder material 
as an indenting tool. 

(ii.) The Material tatted with an Indenting 
Tool (statically). Many different kinds of in- 
denting tool have been tried and many ways 
have been suggested to express tho relative 
indenting hardness. 

Calvort and Johnson * and Kiraok B deter- 
mined tho load required to produce a 
permanent indentation of a given depth, but, 

1 L'Arl lie f-onverlir, 1722, i>p. 20ft nnrt 299. 

Ann. Thus. Cticm. 03, i. 103-108. . 

a " Prism Hardnnss," Tnst. Mech, F.ng. Journ., 
Ont. 11)20. 

4 " HnttlncBS of Motala and Alloys," Plnl. Mag, 
4th Borlcs, xvii. I'M. 

1 iWiUlictluttf/en den K.l: ieelwologiaclien Gtteerbe- 
Museums, Wieii, 18!)1, p. 108. 



whereas Calvert and Johnson used it tru 
cone and a depth of 1J-5 mm., Kirsoh employed 
a cylindrical plunger of 5 mm. din-meter and 
a depth of (Mil mm. 

Tho test adopted in ISfifi by tho Unitnl 
Slates Ordnance Department was a deter- 
mination of tho volume of the indentation 
produced by a pyramidal point under a load of 



E 




r(i7) Foeppl 

I'm, 114. 

10,000 Ibs. A volume of 0-5 eubio inch vim 
taken as unit hardness. 

Middleberg 7 used an indenting tool, in Mm 
form of a curved knife edge, for studying tins 
hardness of tyres. Tho knife edge wjui 
inch long, hnd an angle of 30", and ..wan 
formed with an edge curved to 1 inch radhin. 
Tho reciprocal of the length of tho indentation 
under a loud of GOOD Ibs. was taken an a, 
measure of tho hardness. 

Unwin B also Employed a knife edge, hill; 
in his case it was straight and consisted of a 
pieco of hardened and ground 3-inch sqiiiiin 
steel, 1 inches in length. Each tool tliun 
had four indenting edges having anglen of 
00, The material tested was formed into 
test bara \" xj" x 2" f and tho hnifo edge mis 
placed on 'tho bar at right angles to its length, 
overlapping it by J inch on each side. Tim 
hardness number was taken as P/H, 

whore P = tho load in tons 
and H=tho depth of tho indentation in 
inches. 

(iii.) Brindl Hardness Test. 'I'ho method of 
test devised by J, A. Brmell D in 1000 is now 
extensively employed, A hardened steel bull 
ia pressed under , known load into tho material 
to be tested, and the hardness numlinr in 
taken a tho stresa pen.* unit of spherical arm, 
The reason why Urinell used the sphitrinil 
area is not clear, as there docs net appear 1<t 
bo any advantage gained by using it instead 
of tho projected area (iril s f'\). 

a Itcport on Mctats for Gannon, 1850. 
1 Engineering, IRRfl, 11. -181, 
8 /HS(. Civ. 1'fnir. Proc., 181)7, oxxlx. 
' "Methods of TcsMiiR Steel," Inter. Anmir. I>"-t- 
Mat, Proc., 1001 d'aiia), il. 81. 



192 



ELASTIC CONSTANTS 



If P pressure in kilograms, 

Jj = (lianinttitM)f (he l>iill uwd in millimetres, 
(/--diameter of the indentation in milli- 

inotrc;;, 
A--the depUi of imlenlation in millimetres 

<Hl!*7ff.]15),^ 

tlion A = ^(-v]7a37/ii) mm., 

niul tlio spherical area of indentation 



Tho Jirinell IhmlnesH Number ll^l'/A. 

Tho diameter (rZ) is usually measured 1>y a 
micromotor mieroaeurie, Jiy the IIHO of some 
form* of BrincU inBtriunonts the depth (Ii L ) of 
tho indentation in taken as tho lost proceeds 
(sra (j (87)). With these instrument.'! tlio depth 
ivJiiiih I'M meiisumd in A,, mid not fi (.see ]f\<j, lid). 
It should ho noted tluit, owing to tho rising of 




tho edges of the Jlrincll indentation, /i t ia not 
equal to It, and, as tlio amount (if tin's sido ex- 
trusion is not tho siuuo with different materials l 
imder Hiinilnr conditions, tho ratio of A,/A is nut 
always constant. It tlioroforo follnwa that tho 
hardiiL'8 iiiuiil.Kjr ohtainud in this way is not 
tho liimlnoHH niniilmi 1 us definoil by Uri'nclJ. 

It is found that tho hunlnrsn number vnrios 
with tho ditunotor of tho hall, and pressure 
pmnloywl. JAir Btnotly oompiu-ahlo roHulls 
lixod valuta must ho \isud for .J) and I*. Tho 
values BtiUKliu'diKisd hy Hi'inoll nro : 

1):=10 mm. and I 1 = 3000 kilograms except 
for soft imileualH, whon a value oE 1 J = COO 
kilcgmius may ho imccl. 

(iv.) Variation of Krinefl flardnes.? with 
Prtmsitre and Diameter of Bull. 0. Benodiuk 2 
of Upsala Bhoived thiit within tho i-ango of 
his louts tho value of (Px ^.D)/A ivas nearly 
eimstant, anil that with a hall of diameter 
= !>! and loud of 3000 kilograms Bnncll's 
hiinlnoHs iiinhor=(Px ^/I),/10)/A. 

In order to allow for variation of prcasuro, 
H. Lo Cliatolior 3 proposed tho farther 



Havito lie Mftallurgie, J.OOU/iil. 01), 




.li.lc 



only 



1 in It 

unit. 

of 



][=Brinell hardness minibci 
1,'^luad employed in kilturn 
A, spherical area of tho ia 
(calculated from tho 
in sq. mm., 

l) l =diamet(!i i of tho ball used 
Uoth the equations! suggested liV" 
and Lo Chatolier aro empyi-jcal and. 
approximate values. 

E. Moyor 4 in some published results J'" 1 
showed (.1) that P-mf", whcro iH JL l ' lh]l " 
stant de]iending on the material, 
constant for a given material ami ^ 
diameter; (2) that the mean pressu^o 
area (IP/TH/-) is constant for u given. *~--^- 
mdontation, whatever the rHaiiioUu 1 nf t-lm Hall. 
It follows from Meyer's law of o*ti j wu'iHim 
that, 09 d/[) and P/.Jir^ 13 aro c<*nt*('- rtl11 '' f" 1 
similar indentations on the anmo iniituinnlj 
l'/B a IH alwo eon-stant, 
wlioro 1' -- jij'ossuro, 

(/ = dianietoi 1 of improBsion, n 1 1 tl 
J) = diamotor o tho bull. 
This relatioiiHhip is useful whei-o tho jn" 
material is so small that a pressure; *>T 
kilograma cannot l)o applied with ^b 1<) 
hall. J.t is then only necessary to 
smallor ball and a load determined 
ahovo relation whip to obtain tho 

hardiiOKsnuiiiljer required; thus, if a 1>MH " ' 

l-\)iH used, tho load to bo ivppHiHl in 
Px]V 3000 xfl 2 Hf 



ii.'it) 
1->.V 



-u <>C 
UOlllJ 
tnin. 
a 



Some resnlla obtained hy Hakcr B uutl 

in Table .'U show remarkably good H,<J:J <?<*! DC <ul> 

of (Jio hardness mnnbera olitained in t-Fiin ivny. 



TAIU.I; 31 

.UllINKia, lUlUlWUSS NUMH VJH! M 

KAI.I.S o]-' DIPJ.-BRBHT 



Htcol. 


of liali in 


Diiunotnrof 
Impression. 


J.OJKl. 


un.H.n 




nun. 


linn. 


*),. 


Act. 


A 


10 


6-3 


3000 


wrt 




7 


4-4 


1470 


Hfi 




5 


,'(-13 


7iO 


87 




1-10 


0-748 


42 


fj 


B 


10 


4-75 


3000 


loll 




7 


3-33 


1470 


IfiH 




5 


2-35 


750 


KV! 




1-19 


0-507 


42 -S 


IfiS 


C 


10 


a- 48 


3000 


son 




7 


2-43 


1470 


sow 







1-75 


700 


'Jill 




1-10 


0-411 


42 -fi 


an 


1 fails. 'Vcrcines J)ettiscfi. Ing,, 1008, p (I'lii 
c Just. Meek. JUng. 1'roc., Oct. 1018, p. fj.ju. ' 



ELASTIC CONSTANTS 



(v.) iS'nn of Twit V'/ci.'c and Effect of Time on 
the, licsiilte and lite Applications of the J3riitf.il 
Hardness Teat. rf. Mooro l found that 

(1) The depth of the indentation, in a Briucll 
te.st should nob bo greutor than 1/7 of tho 
thickness of tlio teat picric. 

(2) Tho oontro of tho indentation ahould 
not 1)0 less than 2 times! its diameter from 
tho edge of tlio test piece. 

Tho tiiuo during which tho pressure is 
applied ia importiint. It is found Unit llio 
tinio effect is most marked up tu about 10 
seconds' application of tlio loud, but lifter 
about 10 wjutmds tho ofi'eet is very small. 
Consequently it ia usntil in Hpee ideations to 
draft tho iUriiioll hardness tost clause as follows ; 

" Tho lirinoll hardness tent, where Hpeoilicd, 
shall bo inado with a 10-mm. diameter ball 
and a lour! of 3000 kilograms, which shall fie 
iiuiinlaiiietl for not, less than 15 seconds, Prior 
to testing, tho skin of tho sample- shall bo 
removed by filing, proper grinding, or machin- 
ing at the point to bo tested." 

Among the most Important applications of 
tho MrineH teat are tho following : 

(i.) I'or ra])id control of chemical earbon 
determinations during iron and skiol marlting, 

(ii.) For testing finished articles without 
damaging tho same, suoli as rails, tyres, 
armour plates, giui-harrela of all lands, struts- 
tural steel, ote. 

(iii.) For examining tlio natures of llio 
material in ontiro or broken parts of machinery 
where- Iho making of a tensile test "bar ia 
impossible. 

(iv.) For testing tho dogrco of hartlncsa and 
softness obtainable by tho thermal treatment 
of any steol, 

(v.) For testing uniformity of temper, 

(vi.) For ascertaining the effect of tho nature 
and tomporaturo of various hardening fluids, 

(vii.) For studying tho effect of eold working. 

It has been shown by numerous observers 
(Aat, Breuil, lirincll, Cbarpy, Dillner, Lo 
Chatelicr, etc.) that there is a closo relation- 
ship between the Brinoil hardness number and 
tho ultimate tensile Btraiigl.li of a material. 

Dillner 8 flnda that, in tlio caao of steel, 
tensile strength -in tons/sq. in, =0 x Brinell 
hardness number. Tho values of " " iiro 
as follows ; 



HrliiolHInriliii'.'.a 
No. 


Vjiluo "["(!." llnll 
IVcssiiru iioruirxl to 
tliBlHm-UnniX 
Hull lilt-', 


VttlimoC'O." Hall 
Prrasuro In tlio 
nii-cetlon o! llulllnii. 


Below 175 , 
Above 17C . 


0-230 
0-210 


0-225 
0-20G 



InvestlsattoH on tlio Jlrlnoll Method of tlotur- 
HnriliiiiSft," Inter, Assoo, 'J'cst. Slat. 1'roc., 
1111K), No. 0. 

* " Jlcscnrrihcs conwnilne tho llelation botwcon 
lIurdncsB Kmiilior and Tensilo Strength," Engineer- 
ing, -Nov. 9. 1900, i). 038. 

VOL. I 



Unwin 3 dedncRd tlio following 
from a table uoJii piled by Iludfield : 

T=0'2H + , 
Y = 0-2:H I -Hi-fi, 
where H is the Brinell nml>cr (in kil 

ftq. mill.), 
T = Ultimate tensile nlrcngthin tons ]mr 

sqniiro inch, 

Y Viold stress in tons per sijuuro inli, 
(81) liHINUUr, llAHBNMHH TKSTlNll 
The Urincll hai-dncss ical in iiuiti; 
ly osit-i-iod out in imy uun-'hino iit 
which a pi'OHsuro of 3000 Ivilogi'iuiiH vnn lie. 
necurahsly ft|i|)liod, suuh IIH n, univoraal tenting 
maoliiiHs having n compression aUncslnnent, by 
tho use of a fl|ifji;il tool for holding tlio bull. 

Special nwohmcs liavc, lunviwcr, biicn 
(lovclnpod for tho 
purpose, and 
these are of two 
main types i 

(a) In which 
tho load is applied 
by oil prt'HSuro 
ftnd Dipusured by 
a. proannre gaiiyo 
or lU'iul - weight 
coalrol. 




i-' 10. 



or lover machine- 8. 

(i.) Jack-mail's 
Oil Press u r a 
Jirincll Machine. 
An example of 
tlio firat typo of 
ninuhmo is uliown 
in 7'% lift. Tliisi 
ia tho apparatus 
supplied by tf. 
\V, Jacknnm & 
Co. t Limited, 
Caxton Ifoiiso, 
Westminster, of 
tho Aktiobokgot Alpha (Swodcn) design* 

Tlio ball K*is attached to tho downwardly 
acting ram of n hydraulic presu. The lunt 
piece is placed on the ndjustablo tables S, 
and ia raised into contact with tho ball by tho 
hand-wheel r, Tho pressure in produced l>y 
a small lumd-pninp, and may bo read direuUy 
in kilograms on a pressure gaugo. '.I'ho 
maohino is also provided with a dcad-wt-iglit 
control consisting of a piston, niioui'iilcl.y 
fitted without packing, carrying n tivnm l)iir 
i, small cylinder a, and m-ilit;i p. Tins 
small oylindor ia connected to tho top of tins 
press BO that tho intensity of prcssm'Q in tins 
aamo on tlio piston nw on tlic ruin. Tho 
maximnni pressure) is regulated by tho wolglitH 
p, and when thia pressure iti reanhcd tho 

3 " Miiclmnicall*i'opBrtli)sotMntcrlLila," l)ittl,'Mct'tt, 
JSng. Proa., Oct. 1!)]S, ]i. '132. 



104 



ELASTIC CONSTANTS 



piston rises in the cylinder. Tin; pressure 
remains const ant a4 long as the- piston " floatB," 
funning a small hydr.iiilio accumulator. 

The small piston ia formed by a. slul bull, 
and tlie piston rod has a cup- shaped end 
which proassa on tho hull. Any leakage of 
oil past the piston is collected in a receptacle 
(/, from which it is mturned to tho reservoir 
through tho funnel I. 

Tho pressure is released by opening a viilvo 
v which connects tlio top of the pressure 
chamber with the reservoir. 

(ii,) Avcnj',1 J)e.(nl-wei<jlil JirincH illacJiine.- 
The arrangement of this machine is shown in 
7'Vf/. 117. The specimen is place,'.! on tlio 



is then screwed up tightly, to seonro tlio 
locking plate, / ami prevent tho rotation of 
tho screw. The pressure ifi then applied, by 
means of a worm ami worm-wheel h operated 
by the largo hand-wheel ij at iho Hide of the 
machine, Tho weights p uro " sel: " for tbo 
proscribed load, and tbo lifting of tho steel- 
yards indicates that this loud is applied. 

Tho syatem of levers for measuring tho 
pressure- is that adopted by \V. & T, Avery, 
Ltd., Hirmingham, in all their platform 
weighing machines, and is found to bo ex- 
tremely sensitive- to nmall difl'oromics of load. 

Tho lovcrago of the inaehimi ean bo oiitaitierl 
direutly by measurement, but it is alau 





Via. L17. 



weighing ])hitcn s, ami if. of any coimidorablo 

HI/.O its weight is " tared oft " by moving one 

of the (tliding poifio.s c upoi; the weighing 

etcolyanla until tho woigliing tiystom ia 

balanccii. Tho ball /; ia then brought into 

contact with tho test piece by lowering tho 

screw by which tho pressure is applied. This 

-LINI. f(uieldy by unwerowing tho thunib- 

<it tbo top of tho standard, and 

acrow by the small band-wbool 

iyod to it. Tlio thumb-screw 



calibrated by dead - weight loading on the 
platens s. 

(82) TiU'i JoriNSiiN HAHDNKHH TUHTINII 
AlAOiilNJ'j (maniifactured by llrown JSayloys 
Hteel \Voi i ltH, Ltd., Shetliold).- ThiH maehino 
has been devised to eimuro rapid mid accurate 
working and at tho mimo lime withstand rough 
workshop UNO, n!f|uiro praiitically no attention 
or adjustment, and he easily movable from 
]ihicu to plaeo without detriment. Tho total 
weight of tho maehino is only 100 Ilia., and its 
over-all dimensions a re 28 x Hi! x 9". It will lake 
test pieces -IJ- in. thick, and tho indentation 
ean bu made at (listancoa up to HI- in. from 
tho edge. Tho arrangement of the machine ia 
shown in l''i<J. 118. 

(i.) .Demrijitiaii of HIG JI/firiAi'He. -'Pressure is 
applied to tho steoi ball A by means of 
tho lover 'H ami ball - boaring eoeontrio 
through the single lover .1) mid screw K 
Tho other end of tho lover 1) is held by an 
eccentric in ball-boa rings V, to ono of which 
is attached tho lever Ci and weight .11. 
The weight IT is raised by tho eccentric Ii* 
when tho pressure on tho ball A rcaohra JiOOO 
kilos, and any further movement of tho 



ELASTIC CONSTANTS 



105 



operating lover Ii tending to apply fiirilu:r 
pressure on tho ball only results in raising 
the weight still more. 

(ii,) 'Method r>f mukiiKj Test. The specimen 
to be tested {which must Inivo a smooth Jttit 
surface) iy placed on Ilio table 
I". The adjimtiiig screw K is 
then brought down until Iho 
steel bull A rests on (he pre- 
pared surface of the specimen. 
Tin; lever Ji is then pulled 




forwiird until (ho weight M rises, allowing 
tho pawl J to fall into the toothed sector 
K, winch will automatically prevent any 
further movement of tho lever 'Ii. Tho 
load may be kept on for nny desired length 
of time by means of tho retaining pawl L, 
which is moved in and out of position by 
mains of tho knurled hiincllo M. In order 
to release tho pressure the lever ]J is replaced 
to its original vertical position and tho Adjust- 
ing screw 13 raised. 

(8!)) BJUNKLL PKTKRS. For ascertaining the 
lirinoll hardness of small and thin specimens, 
(malms partridge caseH.IlndgoWhitivoi'Ui, Ltd., 
have devised a hand instrument which they 
(jiill Tirincll pliers, '.[.'hey are shown in Fig. 110 
and consist essentially of a pair of pliers one 
iioso of which servos aa an nnvif for supporting 
tho cartridge case or specimen to bo tested, 



the other nose currying a cylinder lilted \vith 
a piston, ;it the back of which is a spring. The 
end of the? pifiton s!em projects n short distance 
ami carries a small hardened steel hall 11 -^ in. 
diameter. A locking arrangement L enables 
one fo adjust the compression on the 
spring, the usual pressure bring '2'2 ]hs. 

To opcr.ale the instrument, tho H|ieeE- 
men is placed between tho anvil and tho 
ball, and the plier bundles aro grnspctl 
and the procure applied. This brings 
tlio specimen into contact with the ball, 
and forces the )>all and |iislon back 
until tho surfneo of tlio spotJinien comes 
into contact with tho fneo 
through which the hull pro- 
jects, Consequently, the 
actual pri'HSimi between tho 
bull and tho specimen is ipiite 
independent of Iho pressure 
oxorlud by blind, 

Tho dinmeler of (ho in- 
dentation !H measured micro- 
scopically and tlio readings 
are quite definite, even on 
hardened spring sled. 

The instrument found extensivo nun 
__._. controlling tho niannfiicturo of small- 

IJJ'.X.. arniH nmnnmitioti. It Iniit also liren 
omployod for mciifiuring (bo skin bard- 
, IICHS of many vnrieties (if 

sleol (iiiicle!!. 
(H-l) HMAI.I, MACIUNKS 
I'MHTiNii TUB BKINICI.I, 
or THIN MHKKT. 
(.Idodnlc) and Bunks ' do- 
lo] ii*d a " Haby " Brinell 
maoliino for tesling thin sheet, using a ball 
in. in diamolor uiul a loud of Ifi kilogranitt. 
They found that griwt (iiirc had to bo exercised 
in tho manner in wliich tint load was applied. 
Two mothodn of operation ivcro tried, v'm. : 

(1) Tho test piece WHS placed, on tlio nnvil 
and tho bull pressed on tu it until mifllciont 
pressLire was oxericd to raiso tho hahneo beam. 

(2) Tho test pioco was forced, undor a ^iven 




loud, into contact with tho hall. '. 
remained in ft fixed position, 
Tho second method gave Biimltor ami more 

1 "llcvolopinont of Jiriiioll llnrdnnas T<-nt on 
Thin ]Jruss rihcL't," Amcr. tSoc, Tcsl, Mat, xlx. 7fiH. 



19(1 



ELASTIC CONSTANTS 



romills than tlic lirwt, find was 
tliomfnro inunrporiitcd in tho dtsnigri of their 
Him! uiiuiliiiH'. Tho Inittl \VHH applied by a 
(lend weight of IT) Hib?, mid tho tlinmctcr cif 
1.1m iJiipi'tsHHion Wiifi measured with a metal- 
lurgical microHWHio with it Kl-imn. objective 
and 11 lihii' micromotor typii of eye-piooo. 

Siiuilni 1 work lias been <!;imcd out in Eng- 
land; ' tho fmll lined, however, was I mm. 



It JH pHHoriUul for llio measurement of smiill 
indwiliitions that tho re should lit) vertical 
illumination. 

fj(Sft)Tiii'3 Liimnit HAUDNUKS TI;KT. In 
order to overcome the variation in the Jirindl 
hurdmwH number \rilli load mid i/-o of bull, 
Liidwilt - propound Hiilisl.itiitiug n> H<* <>'"> for 
till! hall, mil I thin form of indenting tool is 
niMVofton iiHorl on t\w "Continent fnr tho Hoftcr 
tnolitls. 'I'lm hiii-duoi-m number in obtained by 
means of Uiin Li'st in tlin mmu way nn with 
tlio ISriiiHl TdHt, i.*?. tliti tout loud in Mlogmnw 
In diviclod by tlio Hurfmsc of tlio conical in- 
di'iiliLl'ion lit wj. mm. t HI> that if 

I.'--- tlio load, 
tnul rl dmmotoi 1 of iiuloiitalion, 



-. ,-,, ,1 - ,, ,, - ;n; 
TT(<//^) x (rf/ ^2) 

.--0 n(l'/(/ 2 ) iipproxinmtoly. 
With thin iijuHiratim the Imrdiu'Hg number in 
tlio Htiruo wliatovoi 1 tlio load Chosen, if tlio 
nititi'i'ial in homtigoncous. 

(KO) MnAHintimi JIiciioacoi'MS von HAHD- 
NHHH TKHT.S. ];'IH' coininoi'cjiitl work Ihn 
diiiiuetor E llio iiulontation in nioamii'Ml to 
bho lUiurcHt 0-05 mm., ami for this purposo 
a niiu] i o.'ii!npo with n, scalo in Hie cyo-picoo 




I'm. 120. 

In uHimlly Hiijipliod with tlio Brinoll appamtns. 
To fucilitivtn tlio roiuUng of iniprraBioiia iniwlo 
incornora or liulow the gononil snrfnco of tho 
Hncoinidii, tho niiwiiMisopo in n<)mut.inies pro- 
viilctl with a spciiinl ntlnptablo piece. 

li'oi 1 roHDiiniH work mi iicjouraoy of 0-001 mm. 
m cHHuntialj and an msti'iirnont stuih na is 
Hiipplit^l by tlio t.'iun britl go & Paid Inatru- 
incut f'n., Lid., mid aliown in Fig. 120, is 

1 MIIOIV, "A Mniiill Hull Jrardiu'HH Tratlny 
Miic-IHl!,"/iiN(. ,1/VrA. Kna. Jouni,, Jtin. 1(121. 

3 " llanlin-Hii '1'oHlit," inter. Assuc. Teat. Materials 
JVod., l(l, No. (I. 



necessary for tho purpose. It c<'*ti*" if '* ta V . 
mioro-scopn M clamped to a tube* '-* vl ' 
is .supported by the frainuwoi:k of 1-1> 
mout ami can bo traversod by t-li*" 
hoadcd BCICW S having a pitch" of ****> 
metro. The initirostiopo ii fitted ivH-' 1 ll11 *'!'*''. 
pioco containing cross-wires ami I 
with a special focussing median icmi.. 

{87} DKITJI INDICATORS iron, 
'r.KHTS.Tn order to dispense wifcH <-!*> I1f " ! "' 
a microacopo tlio depth of tlio melon t-ti ti<'i' ''' l11 
bo measured during tho test by m(^i-i li * ( " H" 111 " 
form of depth indicator. Inatritnioii t- H 
typo, which can bo used in any ef 
machine, aro supplied by Alfred T. 
Oo., SchnffliniiBC, 3 or tlio l&iutitifia 
Ccnn|)any, T'ittsbiirgU. 

The doj)tJi lii (Fitj. Hij) \& iii<mHim-l 
relatively to tlio original suvffioo It> ^ l-lio tystt 
piece. 'I'his excludes tlio ofTcufc of tlio tix1't'uni*ni 
rumul tho indentation, and as tlio nnin'ml* of 
plastie flow varies with tliffcrotiti in<i( J-M^ unit 
(Ull'crent prcKsnrcs tlio lu\rdntiH nuinti< i '] 1 n 
found in this way are not propcrt-Lon* 1 -' to t-lm 
Brincl! numbers obtained in tho timial wuy 
from tlio diainotoiu 

(8S) IMPACT OP DYNAMIC Il'-vn MNKHH.- 
Ninnoroiis nicthodB have bocn cl f.\'iHril f*n' 
measuring indeiitatioii Imrdnc'SM hy 1-1 n> HIKO nf 
the indontntion produced by onor(2: i .v <*f Unmvci 
ainoimt. This method in complioiitt'^i by it 
(xnifiidoration of the effect of tho v*stH mud of 
tlio indenting hammer, and thoro i ( I ill'c-n 1 !!"" 
of o])inion asi to whether tho iiiitm L fiini'(4.y of 
tlio Mow or tho net energy nliHorln^ I in pro- 
ducing tho indentation should bn cri>iiHid'n'cl 
in calculating the results. 

Edwards nnd Willis 4 used tho in i 1-io, 1 onoiv*y 
in calculating the results in thoii- i-fH-i'iii'dli "ii 
impact hardness, Uiiwin, G on tlio olhm' 
hand, in of opinion " tluit there nlictnltl 1m a 
sttif^lo impnot and t]iat tho energy of: i'iilii)iiii(l 
should bo deducted from tho cnot'ff.y dm.! to 
tlio height of fall in calculating liariliionn. lie 
doubted tho method of pormittiiijj; micii'i-nidvo 
impncts till the energy was oxpoiicltsel.** 

A dynaiiiio hardness test WIIFI j>i*<i|ioiin(lvil 
by Martel in 1895. Ho used tv ] yrnnihlri| 
point as tho iudentiiig tool, and pi-* Jttmx^ tlui 
indentation by tho fall of a ram oil i*j tho Unit, 
Martel found : 

(1.) That tho work of tlio falling ivim 
jn'opoiiional to tho voluino of tho incicnL f 
ho thorefon* expressed hardness II-M (.lu> \vorlc 
required to produce unit volmtio of i i K 1 tin Ln1 it in. 

(2) That for equal energies of l.il.nv tlio 
voluino of the indentation was near 1 3' Um HIIMU-, 



3 I'rlmrosp, "Iliirdncsa Teatlng," Xti&t. jlfrrh. Kittt, 
Journ.,(M. 1020. 

1 fust. Mcch, ling. Proc., May 10.18, jijt. SJiVH-iinn 
1 " Ilnrilncss 'J'ests," lust, Mecli, JCnt/. /*j-r,. HUM. 

p. lira. 

< Commission eles M&kwles g'KRKin.i rl&ft J\Jnti',ritinx 
dc Construction, I'aria, '18U5, Scot. A, i>. id<l j . 



ELASTIC! CONSTANTS 



107 



ising indenting tools of slightly different 

inithor carried out a scries of expe.ri- 
1 which confirmed the first of MartePs 
HIOHS. Ho showed further (fiat, when 
it 10-nim. diameter ball, the nitio of 
'mimic hardness number (o the Brinoll 
JHH number was approximately 1-C over 
fa of Brinoll hardness from 20 to 080. 
yriamic hardness number was taken as 
ei|i.ial to tho net energy in kilogram 
J divided by the volume of the indenta- 
i cubic centimetres. 

dynamic method ia useful for deter- 
; -the indentation hardness values of 
i nt, high temperatures, under which 
tho standard Brinoll Test cannot 
carried out. The indenting 
i the dynamic test is in contact with the 
inn for such a short interval of time that 
:>~t appreciably affected by the heat. 
19) DYNAMIC) ILuiDNKss TESTING 
:>TK3. A moving anvil block is supplied 
. & T. Avery 2 to adapt their Iwicl pen- 
. impact machine (sco (100)) for dynamic 
~!KB tests. 

O) THE PEI.I.IN HARDNESS TESTINO 
lATus 3 is made in Paris by Ph. & .K 
. and is specially designed for determining 
rdnoss of thin materials. The indonta- 
H produced by a falling bar of known 
: having at tho lower ond a steel ball 

2-5 mm. in diameter. Tho 

release of the indenting tool is 
in-ranged olectromagnotically. 
g (91) TIIK AUTO PONUJE, 
designed by Budge- Win tworth, 
Ltd., and shown in Fig. 121, 
is a convenient and service- 
able form of impact hardness 
tester. It was originally 
designed for testing case- 
hardened surfaces, but has 
proved valuable in testing 
materials of every grade of 
hardness, even pure lead. 

It consists essentially of 
a knurled hollow cylinder C, 
from ono end of which pro- 
jects a plunger P which ends 
in ail adaptor and cap for 
carrying ft J-inch hardened 
steel ball B. Tho other end 
of tho Auto Punch is closed 
by a screw-in end, in which 
cl centrally a pa wl -operating rod : | : x 3 in. 
tho object of which will appear shortly. 
cl the sliding hammer is a spring which, 
o case of the 12 -inch Auto Punch, 
eft ftbnufc ISO Ibs. pressure to compress 

il-swin, "ITnnlness TestH," Ist. Mech. fhig. 

Niv. 1018, ]K 570. 

wintering, sclv. 303. 

if/., AiirllSO, 1017, cili. 374. 



it. A (i-ineh Auto I'lintih n\>rii\# nupiiivs 
about '10 HIM. The intcrniil iiieclinnimu is 
shown iii ./''/;/ '2L\. The ]>hin^(ir is ivdnciiil 
to about .[ iimh diumetcr for about 1-7 inchi'rt 
at itfl inner end. This pnrt of the plunger iu 
small onoiijfh to 
]>aHs right through 
the holo in the slid- 
ing hammer, and 
will do so when 
(bo sliding jiiiwl ia 
moved sidewaysi by 
the pawl-operating 
rnd already referred 
to. 

When the Auto 
Punoh is not in use 
the inner end of the 
plunger rests on tho 
pawl in tho sliding 
hammer. When the 
ball is applied to 
tho article to ho 
touted, and tho 
knurled barrel of 
tho Auto Punch in 
prcasi'd towards tho 
article, tho hammer 
is forced buck, ciun- 
pressing the spring, 
nnd continuing to 
comjiross it nnt.il 
tho taper ond of 
tho pawl-operating 
rod presses tho 
pawl to ono side, 
and allows tho com- 
pressed spring to 
drive tho hammer 
forward until tho 
front face of tho 
latter strikes tho 
end of tho larger diameter part of tho pliingft*. 
The kinetic energy of tho hammer is, of coinw, 
nil up to tho moment of its rclenso, no thai, 
however rapidly or slowly the Auto Punch 
may bo worked, tho energy of tho sli'ding 
hammer will bo the same. This energy will Im 
used up in deforming and heating (.ho hammer 
and plunger where these strike ono anothi'i 1 , 
also tho specimen ami ball. Although the 
energy of tho hummer is practically constunl, 
tho proportion of the total energy delivered lit 
the specimen varies according to the hardm-wi 
of the specimen, Tho softer the specimen, 
the greater is tho proportion of the tola! 
energy spent in deforming it. 

Tho diameter of tho indentations produced 
by tho Auto Punch follow those produced by 
tho lirinoll tests on tho same elas.1 of material, 
If a Hrincll Standard Block is employed lo 
check from time to time the readings of the 
Auto Punch, the latter instrument can hn 




-Plunger 



131A. 



108 



ELASTIC CONSTANTS 



iiH.il sis a {|iii<sk way (if aHeoi'lainiiig tlio 
ii|jpi'o\iiiiRli' lii-mi'Il hardness. in cases wlieru 
un Aatu .I'unc'h is used to ascertain \vlintlior 
deliveries are (<i the specified Brinell hardness, 
if; in wwur to UHO Ilii! Aiil.ii Punch un a " wnrk- 
n!mp " (range 1 , anil 1i> employ tlio IMnol! 
machine an mi " inspection " gauge on all 
H|ii!imiM)8 whhsh 1,1 1 o Auto Punch shown 
(.< lio iimr nno or other of Iho limitn of 



iiwtruimmfc for measuring hardness. A Hiitall 
diamond-pointed hammer about .] ineli long 
anil .[ inch dumietor, weighing Vif o/., is allowed 
to 1'iill friidy from a height of lf> innhes. The 
Imight of rebound nf tlio hammer in measured 
njjiiinat a Hculr, graduated into blOeqnu.1 parts, 
uiid i talicm IIH a measure of the hurdncHS. 
Tlw sbapn of tint diamond striking point id 
Mightily Hiiherieal and blunt, being about 0-020 
iiuili in ilintn^L^i 1 . 

Tlio in.il.nim<;n(. iti one which d(!|MidB on 
tlui [H'odiidlion of a porimmont indcintalion 
liy I'liisi ]]oint, thn rolinnnd Rising diminished 
hy llin wiirk (ixj)Qtuloil in jimilucing tlio 
induntiilion. AVith ru liber no jionnanonb 
imlcnl-iitioii is pi'oihicod, and tho height of 
roboiind SH tin* flunio us that from a moderately 
hn rd Hlcsol. 

Th iimtrn niont ifi providod with nn ingnnious 
iintomiiliu liond by moans of which tho hammer 
IH litUid and relcuHcd by nil' pressure from a 
In i!b. 

Tho HlonHC<i|o and Brinoll liardiiosa scales a 
Itavo liftpn nhowii to bn yonoi'ally closely related 
il Lho hurdncaa range. Tho Brinell 
munliisi 1 divi<lud hy six is npjmm- 
]iialoly ii(|iial to tlio ftoloroscopo iniiidinr ; tho 
rivtio up|'iH' to intireaso from C-o for soft 
Hkiuls t H'O for inaUirmls of over 700 on tho 
Hrincll Hcalo. Tlio [ippliuulimw of tlm Scloro- 
,s<'it|ic iirci tlnnxifiH'c. Hiniilar to tlioHoetmmoriitod 
forllKi JlriimlL CoHt in (BO). 

'I'lai Ktslisi'dBoopo i-diuJinif!] have hceii found 
fa lui ulighl.ly {Ji(])i!iKU)iit uu tho Hi p /:0 of (ho 
jiiiMio tisslnd. This variation can ho c<m- 
Hidorably rotUiccd by o lamping Iho itJHt piece 
tn ft linn foundation. Host materials arc 
iiKHiimnii-ally linrdcncd by indentation. It SH 
tlinrofiiro iinpoi'timt t<i onsiiro Hint (ho inatcriiil 
i.s nob ioatii'd twicio on tho same place, otherwise 
liitfli rifHitltn am <i1il(iincd. 

(Oil) AllHAHlON Olt SORATOJI TESTS. - TIlO 

nhninifJii li'Ml IKIH boon applied in thrcu ways : 

(I) AH a Hounteh lcb. 

('>) Jly drilling or grooving with a hardened 
H(M<| l:ocil or dmnmnd. 

(II) Hy vvoai'ing a\ray M'itli or without an 




lt Wil ' V 



Jj'OH) Tins SniUTcn TKST. , ,., - 
has buoiifi'c'qnontly used in eonjimediiJ 111 vt ' 1 
indentation hardness test. In 1722 l-I*'^ 1 *' limi " 
used both methods. As an iiulitf"-*-' ''*"' ' 
scratch hardness ho tested metals ri|Jt' 1 ' I1H1 ' '* 
bar whoso hardness increased from *> Ilt1 /'"'I 
|,o the other; tho position on this In 1 - 1 -" 
the metal under (.cat would scmttda 
its hardness. Jlohs ' was tho 
scratch hardness scale, which is 
used by mmoralugifjta. Ten 
arranged in order from 1 to 10 in. mi 
that each would scratch tho 0110 iit : 
it on the list. Tale wna taken UN 
hardness of " 0110 " and diamond ji 
of " ton." 

(i.) Turner's MderomelerP Tii 
a balanced lover is 

(1) Provided at its free cud with it. 
point fixed in a vertical pencil, 

('2) Loaded with a sliding weight 
bmted in order that tho sliding wt: 
ho not to represent known weight: 
point. 

(3) Supported in stick a way that 
rotated. 

Tho hardness iiumher is tho ft 
in grammes which will produce a 
visible to tho naked oyo on tho sn 
polished surface of tho specimen. 

A series of scratches are made with <l IIM ininh- 
ing weights, and tho hardness iataU*'ii in thrt 
mean between tho least weight 'vi-lii".'!* will 
produce a scratch and tho greatt,'nt >vtijht 
which will not prodnco a scratoh, 

A. Martens, in order to inako tho t:<*nli iimni 
definite, defined the scratch hardno.MM rmntlici' 
as the load in grammes under whiesti n t.'inii p id 
diamond (00) produces a scratch O-Ol mm, 
in width. 

(ii.) A. L. ParHons 7 further, nior] iflfil tin 1 
Scleroineter by applying tho loud oil 1 1 IK 
diamond point by a spring in suoh a. Av**.y (lint 
tho pressure increased as tho point \VIIM e Iruwn 
across tho tout piece. The plnco ivfc ^vliiiih tin 1 
Hcratob commeiK'ed wna noted, and tl*** CHITO- 
spontling load was talcen ns thu } i ] i I'dnrn i 
numboi'. 

(iii.) jf'/ie Quadrant Sclei'omc.lftr. - ~ Thin 
instriiinotit has been devised in tliti .J t,inlf.;it- 
Whitworlh Laboratory. 'I'hc niethoil isi n |j]iiyetl 
is to api>ly a hardened edge or BoL'ios <if lin. rilened 
edges to tho surface of the teat ])it;<:o i u nin-li IL 
direction that (dipping ensues until tlioy * ' hil " 
the surface of the article. 

Tho instrument IB mado in vnridtiht tyjn-rt 
for testing either Oat surfaces, piiiw, *i-' tin: 



**!-' 

<'"ti lie? 

\voifrhfc 
-*'! 1 jiint 
'H 1 ' 1 ' und 



3 L'nrl de Cativerlir, 1722. pji. liflfl iiurt H. 

' Uruwlriss tier Mineritlogie, ISHSj ]>:irt- E. 
374. 

' flirmingliam Phil, floe, Proc.. v. purt 11, t i KH'/ 

8 NitzuiujslierleMe ties Vcrcinea zit-r -flf'JTi'Ji'.t 

lies flaieerbfleisses, 388S, ]). 41 , nncl J.88O, i*. ] ^17, 

1 Amer. Joiini. of Science, Feb. IfllO. 



ELASTIC) CONSTANTS 



inn 



inside of cylindrical mnfaces. /''/;/. 12i> .shows 
a pin inuloi' ((;,-!L. 

Two s])ijciiilly fliit flat rods or lil;^ I* 1 , anil F., 
arc employed, and tho upper OIKS h rnisoil until 
it makes an aiiln of about 80 with tlic low<;r. 
The |iin I 1 is then placed between thm and 
tlio " filii " lowered until if, " Mica " tins pin. 
The angle at this point is an index of tlio 
scratch liardiifwH {>f the article. 

Tho theory of iho iiiiitnirnnnt lias beon 
worked out by II. L. Ilealhnoto, 1 who IIHS 
shown thai; tlio anglo is practically independent 
of tlio weight a-nd HI/.H of the article to bo 
tested, A soft 'bar holds thn top file up BO 
that it midcca an anj.de of about 70". A hard 
hai 1 will nut hold thn top file up until the 
angle falls to iihont If) to 20. Hardened and 
tempered burs give readings between 20 and 
70, according to their surface rcsista.iicc to 




abrasion. Tlio instrument can also bo em- 
ployed for measuring the coefficient of friction 
between ono material and another, one being 
attached to, or substituted for, the upper, arm, 
and the other for tlio lower. 

(95) " Diur.r.tNCJ on GKOOVINO" HAHD- 
NKSS. H. Hottono a measured tlio resistance 
to wojir as the time required to produce in tlio 
material ft cut of definite depth with a auft 
in)ii tliao rotating at constant speed and preaaod 
with constant force. 

A. Hmisanor 8 doflncLl oiitting hardness JIB 
the resistance, per square mm., to planing, 
when using a cutting angle of 90, 

Jaggar 4 rotated a diamond point under 
constant pressure and nt a uniform rate, and 

1 Iran and Sled Inst. Jaunt., May 101-i. 

llolation ontro lo i>ulilH atomifiiio, lo liolila 

al Neivs, 



(it la. ilurcti ilca corps," Ohemital 
1873.li.21B. 

3 " Das JDibcln voa HotalliMi," MM, fas I'. 
taclittoloff. Gcu'erbe-Afitscunts, Wtan, 1802, II. 117. 

* " A Jticroacleronioler," Ainer, Joitm. of Scienc 
Doo. 1B07, iv. 81)1). 



thf! nuinbnr of nihitions nt tin; poinL i.o 
rciitli a (ixed <k'])th aa tho liartluesH. Itauet 
and .Ketij) s liotli defined BiiLlin^ luu'iiiMwa us 
the rale at whieh a Hti'ci drill, running til. 
constant spiscd and under onnstaiit ]ii'oasiiK', 
drills the inaienal. 

(DO) WKAH TISSTS. (a) lining an abradant 
or an abcading wlicel (pure abrasion). lYitix 
Itobin niiuiJ cyliiichicnl specimens (HO mm, 
diameter), which ho ru)>iid undei* IUKHVII 
])i'OHMiiro on papers 1 covered with abrasive 
l>ivdera. Kfisiwa.ll ' dclined nlirasive litirdimas 
as equal to (1/loaa of volinne}, by grinding 
\vitli an abmdiint. liohreiK? B used a- standard 
pnwtJer mid inonsiired hardnoss by tlio time 
requircfl to polish. 

Gary determined the resistance to wear 
by tho amount of abrasiioii isansctl by 
u santl- blast, nnd cxporinienlfd chiefly 
with stones, artifidul minerals, find tiinljcr. 
VJ. If. AVarrcn 10 also used tho sand-blast on 
timber. 

JaimotfiK ftnd Crtildber/Jf, 11 and Hrnnghton 
and Ifacgregoi 1 ia aneasured tho comparative- 
li>a by grinding, ',1'ho latter, who nl.io curried 
nut hidontiition Hiardncss Ira Is, fciund that 
tlio two inetlioda gave difl'oroJit uoinjianitivo 
reaulf's. 

(!>} Wear by nlulin^ hiln-u:nied ulirasion. - 
Dorilion ia eiiiifttriiolntL a nia<;hine iti which a 
specimen was pressed on to tlio cii'euinfercnro 
of a polishiid wli(!(il turning ad n Hpuisd of 
;ii!l)0 rovohiliiMis per ininnto in an oil hath. 
The wear was nifmmircd by the l<wa in weigbl. 
or reduction in diameter in lluniHandths <if 
a millinictra lifter 2,000,000 turns of thn 
wheel. 

(c) Wcnr by dry rolling aln'asion.Siinitdr lu " 
devised H machine for testing the) wearing 
pTOperties of rail steel under dry ruHing abra- 
sion. In this method tho specimen (A), fi 
inches long and 0-5 inch diameter, ivna fixed 
inac!mck(Jl, /''iff. 12;j)j i ovolvmjrat'1000r.p.in, 1 
and carried near the freo end a ball-bearing (Oj, 
of inner dianietor-1 inch, loaded to produco <i 
presauro of 205 Ibs. at tho point of contatit. 
The inner ring of the ball-bearing (I), } inch 
wide) was rotated by friction by tho test pieou, 
causing the latter to wear. The resistance of 
tlio material to rolling abrasion wns ta.lt en as 

J Krcp, "irardnRSS nr tlift Worltalilllty of Molnls." 
Amer. Soe. Mech. Hug. Trunx,, lloo, 1000, iibatract in 
Iron and Steel Insi. J,, 1001,1. -198. 

I Iron ami Nleel fnsl. ,/., 1011). 

7 Verliand. ft. 1: deal, nuinhmislalt, 1800, xyil, -17r, 

a Anleitunfi z\'.r tnittrockemisebaa '- 10 " r '- 

3 Baumrilerialicnkn.ntle, x. Jllft. 

10 " HtrciiRth. Jllasttfllty, iiiul 
N.S.W. Jltirclwnoil I'Lniliei 
Foffstru, A'.S.W., 101). 

" Assoo. Prune. j>. I'Aranc,. 

u " ItaTtlnosa TcstH," Awei 
mi, xi. 707. 

" See Nuabanmcr on "Notes DI 
.Uctnls," fitter. /Issue. Vest. AInt. I 

II Iron and ,Ste'/ fast. J., I'.IUB, 

Assoo. Test. Mat. Prue. ii. No. 0, pa. , . 



200 



CONSTANTS 



lining inversely jiroportimwl to the reduction 
in diameter in tfii.tliouHiindlhs of an inch 
after 2()l),(mO rovolutiojiH of the tOHl. pHscso. 

A Hiriiilar li.\4(, way iiaoil by iSliinlou and 
HatHon. ' for a HW'HIH nf experiments on hanl- 
nt'HS tiiHta. The dinieimionH of tin; test piece, 
(i((!., won> made slightly larger Hum those 
f.irii|)]oyt;d liy Kanitur. 

.11 wan Hliowii that the I'osiKtiiiico (,o rolling 
wan approximately proportional to 
Llio ball hardnoss number, but that tho dom- 
puriMoii WUH not a tiafo one, as there wore 
tly dimc'N in which a considerable do- 
was found from this ratio, e,<f, inan- 
Hteol whieh WiiH well known to 1m 
iblu to Imrdtmiiig undor pressure. Tho 
(jonlinned Hnnilor'a cfiiKilii.'sioiin, mid 



rihir.'i!! 
HUT Mm 



ToTiiaining fixnd relative l tho iminli '' l 
.slip jusr rovohitioTi was thon=^ [) ft') iJi''!" 1 ''' 
Tho results indicated tlinfc there \va -\'** r '.V ''"''' 
liiu'doiiing of the surffieo of Uio nitJ"i JIL ' lll|lle ' 1 ' 
UIOHO conclitiotis, and that tho UriuitLI ln 
nuniljur was not a Hiifo guide in prnf li*' 1 ' 
relativo rcsistanaoa to wear of n, miHC** 
Holoction i)f steel. 

(fl7) IMPACT AND No'rciiRn BAH 
Thorc ia no doubt; that tho tonwiU> ' 1 .' 

usually carried out, does nob givo *--" *'''" '"" 
fiirmation ahinit a material it in e.^H 
tin engineer should know. A careful 
tion of a complete load cxtonaioii 
however, revealu differences, aiioh as 
to Iieab treatinoiit and incchnnioal 
not diacloactl by an ordinary tonsrl(. 



1.1mb 

L xmnimi- 



Speeding u/i Gaai 
running in tut of I datli 




. Qear Wheel ilrioea by 
an Electric Moto 



ever fur npp 
lie Load 

.0. jrin 


tjlntj 
~~^*t- 

D > 






-( 

w 
PL 


y 


^r 1 Y- 











L.L L. 


* 






1 B i 


'A 


$z 

' 


i 

1 : 

>;- 





Itall- 

tiaarlng- 

Carrier 



penemto. 

It h(lH * jT!l.lllHL<in- 

ally, hurjii f<nmi] 

that n iMfi,(<-rml 

toi'ily p.ivHH"< I 1ho 
ordinary ttMU'i '*' I'"*"' 
fni'ls in 
11 

cntinotl)ii<!<^ ninl-i'il 
fr by orr**! 1 ^ i" ( l"- 
Higu. J twcsvl'ijCiUtm 
has Hhnwii i.littl,, in 



\vhi 



Via. 123. 

wliownd that wliab was uctiially meaniu'cd was 
tho H'sifitiinoo to diHiiitognition of already do- 
Jorimid inatoiiiil, and. that tliia roaistantjo 
4ln|imidi l il on tlio iimoiint of defDrmation pro- 
duircil, and had little relation In tho material 
JEL Uni unnlmiiKid condition, 'I'he niethotl, as 
a numna of jirodioting tlui rnlativo rosiatanuc 
ti> wear undei' eonditkina of rolling abniwion 
with heavy loudH, wns ooinpumtively rapid and 
HIIVO the iiifonnatiim dcnired. 

(tt) Wrur by dry nluliiig abranion. The 
iSiiiiiloi 1 tout M'HH curried out with Jiiyh presauro 
iiml very xinull relative motion. Htanion and 
.Hatnon ' alsn carried out a soric'B of tests on 
dry xHtlinii abruMion, in whieh tlio amount of 
rohUivo motion wan htrye and therefore eorro- 
Hjinndin^ tit tlio wour of ]inn, collni'H, etc. 
Tli in wan (liino ]>y nonnesting tlio abrading 
I'injS filiJiiiicl.iM':" I)) to iho ehuek hy moans of 
mi Oldhain (KMipltii}.', no that both ring and 
jpiioiiiHm (diaiiicl,i!r = "f/) completed a revolu- 
liiun in tlio Hiirne Linin, the line of contact, 

1 " Iliirilnni't Ti'itlrt Rraivircli," fast, Mrch. Kno- 
("TOO., Nov. HUH, p. 0(13. 



have (nil tut I 
way IKI vo I)' 

j octet I L( lllltmlitL 

Con H n q 11 *^ n \> I y, 

various methods of test have bcm <Jc* vii'tul (i> 
givon definite indication of the Hlioulc-i'i^ustiii^ 
properties of materials. 

(98) NoTtiiiHi) JiAii TESTS. 'LiYoocli titi fnun 
tho tendency to crack at nharp unriic^rH, \vbcn 
Lho variations) of Htrcna are oonmdorji,! !% in n. 
property which is very dcsiniblo iix 111 jit-rinln 
for ongincoring work. In order t olit-iiin (bin 
information aliout materials " bril^t.litiic-ris 1 ' 
tests, in which the test piece in iiotdin-t L 
to limit tho plane of fi'acturo and t^lii- 
traction of arcji, are oniplnyod. 

Those notched bar tests a,i?o minlo in t (Hiinui) 
or bonding. Tlio test piece, is usually tr<hki>ii 
by n aiiigle blow in impact, and tlm *^i i ( i ^v r "f 
fracture obtained directly from the* 1 utn nf 
energy of tho striker. 

In lOOfl, Oharpy, 3 in a report on inipjxtif, h'tihi 
on metals, shows that a static toMmon di\tt in 
moro efficaciously suppbinentcd liy IL mf-nl 1( . ( l 
bar bonding lest than by any ollmr Itn'+d.^ and 

1 "Ofllcinl Ih'porl on Tiupuct '1'e.tls <f fl| t ,\ ,,(,, 
Inter. Assuc. Test, Mm, 1'foc.. 1000, Ne^. f ^ INH'M.P 
ill./l. ' ' 



tin t\.n 
cou- 



ELASTIC CONSTANTS 



201 



Ilia riisnlls snem lo indicate that the notched | 
hill 1 bending tout gives information rcgardin;; ' 
Miii fragility of materials which other I eats do 
not easily furnish. Oharpy in the ssmio report 
shows that iimtorials which give good results 
with this impact tost luivti stood well in 
practice, whereas the same o.lasa ol materials 
giving low vnhifs fail, although Iho results 
from the ordinary static tensile test is the 
name in both rasitf. 

The originator of this method of testing 
appears l have been M. Uarba of Lo Crcusot, 
win) in 101)0 described tho results of Inn ex- 
periments on tho detection of biittloncHs in 
slocl by tests on Hat specimen.^ notched with 
a 4C)" notch on both Hides to 0-IS5 times tiio 
thioknesa, tho radius at the hottom of. the 
notch being 0-2 mm. mid the total width of 
the specimen 110 mm. The specimen was fixed 
in a hori/,nntiil position between jaws, with 
Mi noliih directly over tho edges of the juwa 
and having a pieco of the specimen 25 nun. 
long projecting from tho jaws. Tina piece 
was struuk hy a falling weight of 18 kilo- 
grams, Kadi specimen was provided with 
ji niinibm' of notches at spaces of 25 mm. along 
the spcoiinon, and liy making a series- of tests 
at different heights of fall it was possible to 
praliet the energy of blow whioh would just 
Invak tho specimen. 

It was siion realised that tliis mothod of 
testing revealed marked diiVe-rencos in tho 
behaviour of materials whioh wore not <le- 
tnotcd by tlio ordinary tensilo test, and other 
mvesligfttm-3 (Lo Cliatelior t (.'liarpy, i'rejnont, 
oto.) carried out oxjioriinents, tho result!) of 
which wero communicated to tho Congress 
of the Iiitoniatutiuil Association of Testing 
Materials held at Kudu 1'estJi in 1001. 

Tlie report oE a isnmniiHsion, apprrtntcd at 
Miis congress to investigate the notchorl bar 
test, was I'lisciissRil at tho congress hold "in 
liriissolH in HXHi, but no ndvnnco way made in 
the matter of standardisation except an. op- 
pression of opinion that Iho test gave in- 
teresting information. Tho florin an Associa- 
tion for Mftthods uf Tosling Jlalcrials thore- 
iilion took tho matter up and issued a report 
in 1!!07, in which they reoonimendorl tho Olmrpy 
method of testing. Tliis consists in tlio MSO 
of a notched specimen, SOxliOxliiO mm., 
supported horizontally at tho ends on knife- 
edges of givon form and struck in tho centre, 
opposite "the notoh, by a ponduhim. Tho 
notoli was formed by drilling a liolc 4 mm. 
diameter in tho bar and sawing through from 
ono side, leaving a depth of 1C mm. behind 
the notch, as shown in fig. 124 Tho span is 
120 mm. 

Tho question of notched Imr testing was 

* again brought forward at tho International 

Congress hdd at Copenhagen in 1000, who 

recommended tho 30x30x100 mm. Chai-py 



te.st piceo, with an nlleniulive specimen, 
eoinoti'ictilly similnr but (mii-Miifd of tho 
Km; when; tho larger dinieiiKionH could not lie-. 
obtaincHl. Tlic inuiter was further discussed 
at New York in 11)12, und the niuonmiomla- 
tions of 1900 were coniirmud. No pnrtieiilar 
machine for carrying out the U-H(M was Huleetccl, 
but further tdsting research on apparatus? and 
test picoi'S of diilei-ont Ki/oa \vnx siigycstcc] an 
being demablo, 

The rocommpiiidatiohs of tho Inlorniitiniinl 
A.SHiiRiation for Toting Materials have nnvor 
boon fully recognised. I 1 '*"- 1 most test \vorU 
the Htaiufnrd 30 x ,'tl) x KiO mm. test pieisn Ims 
been found to be ton large, and [Jiliioiiltii-a 
lnvvo been experienced with tho noteh of tho 
yeomntrically smuller test piece. 

Fremont suggRHla a test piece 10 x 8 x SO 
mm., placed horizontally 011 supporta 21 mm. 



Striker 



Test Piece 




All dlmoaalona 
In iHllllnnitres 



span, wilh ft flottih 1 mm. dee]) und 1 mm. 
wido (squares shnjie, nnd mado on tho broad 
aide at tho cunti'o of the length), Wiy, 
125. 

In moat eases a lost pi ceo 10x10 mm. m 
cross-section is need, but tlio form nf noleh in 
varied. Severn! well-known types of notch 
are given in Fig. 125. Tho beam test jiicwoH 
aro uaually CO mm. ling with a span of 
40 mm. 

(00) NOTCH ui-> BAII THSTINO m BKITAIN. 
A considerablo amount oE work has liei'is 
curried out, in Britain, on the notched Iwu- 
test. Yarrows developed a notched bar test 
in 1002, in which tho test liar wna broken by 
more than ono blow. Valuable inrormatiuii 
appears to have been obtained by Ibis test us 
to tlio bi-ittlcncsis of Htcelfi used for cimiuKslimj 
rod bolts. 

In 1903, iMirt 1 intrnducod a Ringlc-.-blovv 
notched bar testing inaeliiiio, in which tlm 
specimen is held in a vicn ftt ono cud and in 
struck by a falling pendulum at tlm otlwr. 
Thia motlwid is tho one ivhioli is oommoiily 
adopted in Una country at tho presnnt 
tinm, 

l>t. as, llKl'.l. 



202 



ELASTIC CONSTANTS 



Hwitmi and Juili* ' curried out sumo lo-its in 
1!)OI, in wliiclt tin- icHt pit-lie wits broken liy 
u number of Mow*, Mm test bar being reversed 

i>nl,WOim HHCUPStKivO lllllWH. 

liMflUH, Stmiton anil Buiratmv 2 and Har- 
bord :t umnmiminited rosulta of experiments 
to tlm liiHl.iLii(.ioi) of Mtxslumienl Engineers. 
Tlio iiuiiii ]iumt brought out by llarbord'si 
paper wan iFm variability in the results of 
individual lonla of specimens of tho same 
nmleriul. l.t waa 'shown that two identical 
lent pieces from tlio aamn bar of ordinary 
l si nd gjivfl results varying froiii 



I 




Clmrpy 



Mesnager 





Izod 



(OltHonsfoiia 
In inlllliuctfoa) 



U.S.A. 
Bureau of Aircraft 




Fremont 

1'IG, 185. 



ol-liiii' by over 00 ]icr cent, linn varia- 
liilil.y luifi budii uttributud to 

(1) Tho rnudo of tetiiig. 

(2) Tim lieturoi-oiioity of tho inatorial inulor 



[inbliwliod by CJlinrpy nnd C'ornn 
Thoimixl ' show that by careful solcdtion and 
lioitt trontincnt it is |ic>sihle to tilitnin, in tho 
RUTH-HI) uf oxpeiinionts in nutobod bar tests, 
(Jiii'i'ied out on bars of stool of different natures 
or (if (supper, a, dogrco of uniformity antilogous 
l.o (hat obtained by means of tonsilo or liard- 
iiosji liiHts. Viiriability in tlm results is thoro- 
fnro not duo to tlio mode of testing but to 
(lilVoi'onooH in Lho inafnrial under test, 

1 " Ttri]iiu:t TcHlH on \Yroiilit Sleola of Commci'Co," 
I nut. Merit. Kity, J'nw., JWM. jit. iv. 1IU5. 

a '' lt(iHlH|.iuic of Mat.'rhilH to TiiiiinisL" lust. 
jlMf/i, htvj. I'roe., JSov. 20, lODS.nnd lleme do Mcttill., 
Jdu'iili (IlllU. 

" " t)llt'flri)iit niotlioilii of Imimot I'cstlnu on 
N]l(ilii!(l HmV I ml, Ateeli. ting, /'ran., Oct.- DM. 
jIHrH. 

1 " iVow UxiiorlMimils on Slioi-k 'l.'ct,M," Iron and 
Heel lust. Journ., No. 2, 1CH7, ji. 01. 



By li)l-l- them \\-nx 
Ihiii-o wiulil lit! Inrjro variations in ||K 
of notched spcomienK of 
hnpfiet, ivitbout any Rorrefsiiondinj? 
iniuiyof thodiiiriuitemtics brnn^hr 
orcliniiry ton.sili! 1:eat, and tbnro WII.H 



tlj ' l( ' 

Il)l(> " 
\K t-u 



',V 




. Radius 
fytniu. 



that tliia variation was duo to cctrrool. DP 
incorrect heat treatment. 

{100} IMPACT TKSTINO ArACEiiNn.s. < I. J '/'An 
hod Test, Tho IKOC! impact tost hns of i-Hmcpnii 
years come into great prominence in O* vorn- 
ineiit apRoiCicntions, owing to the great c t<: 
made by war oowlttions. 

'I'lR' oi-iginul Ixorl iniiehino had a 
energy of lliehftninior 
of 23 ft.-lbs., and tbo 
test piece was 2 in. 
long, gtlis in. wide, 
and -/'otha in, thick, 
with a veo notob 
O-Ofl in. deep. 

The present stand- 
ard miiduno inndo 
by W. & T. Avory, 
Soho Foundry, 
Binninglmin, ImH a 
capadtyof 120ft.-lbs. 
Tlio cross-section of 
tho test pieeo is 
10 x 10 mm, mid it 
is notched with a 
45 vco notch, 2 mm. 
deop with a root 
radius of 0-26 mm, 
Tho machine is 




Ij'ioi. 127. 



shown in Fvj. 120, and consists of JL Uotwy 
base 13 on to whioh are bolted two ftLrui(tm-ci*u 
S,, S 2 supporting tho pivrit of the pcmdii lum. 
Tho ponduhmi 1> swings on ball he 
strikes tho specimen bold in tbo vice, 
fashion, its point of contact with bho 
being a hardened ntcol knifo odgo. rrjio .fuj-in 
iind angle of tho knife-edge is shown in l**if/. 127 ' 
i'lio apcoinion is gripped in a vieo V in " 



13LA8TIC CONSTANTS 



203 



level 



position tluit the bottom of thn note! 
witli tho lop of the vice, 7'Vr/. 128. 

Tlio specimen, in being broken, absorbs womo 
of the energy from the pendulum, which if! 
measured by the continued and diminished 
swing of the pendulum moving an idle pointer 
over a yratlnatwl scale. The pendulum swings 

10 X 10 mm. r\^ Direction of Blow 
Test Piece 




less aa tlio resistance of tlio specimen is greater. 
This sonlo is graduated to givo the aetuul 
energy in fool;-pmmds absorbed by tlio blow. 
Tho standard throe-notch tost piece is shown 
at U iu Fiij, 129. 

(ii.) The- Clmrpy Pendulum Machine. The 
BTiiall Oharpy machine haa a power of about 30 
kilogmmmotrca (217 ft.-lbs.) and a maxiimim 



A. Beam Typo Test Plcco, 
(Cluirny Metliod) 




C. Enlnrficd View of Notcli 
for Beam nml Cantilever 

Type Test Pieces. ., . 

B, Cantilever Type 3 NoicLi 

Test Pie co. 
FIO. 120. (izoil Method) 

striking velocity of fi'28 metres po-r second 
(17 ft. 4 in. pov BOO.). The principal part of 
tlio pendulum consists of tho hammer M, 
sliapcd as shown in ]fig. ISO, and siis]iondccl 
at the end of a light hollow bar. 'Clio centre 
ia suspended, on ball-hearings, and an index 
hand is mounted with an ousy friciional fit 
and travels over a graduated semicircular dial 
with the hammer when this rises up after 
fracturing the tost specimen. The latter is 
held m cast-iron supports in the two uprights 
which are bolted down tu a cast-iron bedplate. 



'['ho hummer in raised up ffir.K-Uim liy Imnd. 
and IK held up by a catch opt-md-d dmnsl.ly by 
a Hinall lever .1). Tht; drop is conslnnt mid 
1-420 metres (4 ft. 7jj- in.) in height. A 
hand bnilic 11, worked by tin; liiind lever (', 
enables tlio hammer to ho HtoppH rapidly 
after fracture of the BjiedniKii. 'I'lic weight nf 
the falling parU, jioHitioii oi (ha donlre of 
gravity, and hoighU of dro]) csoiinted from (be 
eiinti-o oi ymvity, are all dolmninod e.\iiori- 
nu-nfaliy. Tlio Jingle of IJHU after [uiutiin; in 
read oil from tlio graduatwl seinifirclo. Tlio 
difTeronco botwucn the height of fidl hiiforo 
fraet.ui'o and rising hiiok nfter fimsturo givoa 
the worlt absorbed. It is, however, injocfssnry 
in research work- to laltc into nccount Lho fric- 
tion and energy absorbed by the fragments of 
tlio tent specimen ; the latter may lie; lioiifiidisred 
to take iho siuno velocity IIH the petnlulunii it- 
pelf. Tli weight of the lest fi[i(jtfimcn lining very 
light compared with tluit of (,ho pcndutinn 
hummer, the correction i.s very sliglit nnd cmi 
be neglected in ordinary practice. 

In order to determine the. work absorbed by 
friction the pendulum in canned to oscillate 
freely and the dotmmso in tlio oHcilliitkmH duo 
Biildy to friotion in noted down. This givea a 
tulilo of coiTccliniiH. '.rhe i L ci[iiii'(itl correction 
cmi also be arrived at by noting the angln of 
rise of tlio pimdidum folloH'ing tliiitcautting the 
fracture. 

A larger machine is inndo, mid this lias 2(10 
kilosniininelrea energy nml a Htriking velocity 
of 7-8 moires per seound. 

(iii.) Gitilifin/ Machine (Koturi/ Tup). The 
latcHt niodol of this machine is shown in 
tfig, 131. It (sonsiHts of Jt flywlicel liavhiff d 
" breaking km'fo " attuehcd to it. Thin knife m 
arranged so that it can HHHIIIIKS two [loHitioiiH : 

(1) Hidden in tho rim of the wheel. 

(2) Projecting from the rim (if the whcol in 
\vhiuh position it is reipiired for breaking tho 
toat piece. 

Tho position ia controlled by "studs" on 
the en sing of tlio machine find operated by 
centrifugal force duo to the rotation of Mm 
wheel. 

The rotation of the flywheel operates a umall 
centrifugal pump which elevated a coloured 
liquid in a tube. The machine ia designed HO 
I hat when tho liquid ia at tho top of Lite tiibn 
(and reading /ero on the energy scale) thorn is 
(10 Idlogrammetrcs of energy in tho llywhrel, 
When tho flywheel ia still, and the liquid is 
at its lowest level the reading is thoreforn (10. 

Tho test bar is planed horizontally on Itnifo 
edges which have- a 40-inin. gap, Tho front 
of tho machine is covered with a door which 
ia automatically locked U'hen tbti "knifo" ia 
out and tho- flywheel in motion, 

The test is nmdo by rotating tho flywheel 
to a Hpned slightly in oxeosa of that eornwpnnd- 
ing to the zero of the enoryy Hciilo, Tlio gear 



204 



ELASTIC CONSTANTS 



IH then dii:miiie<!led find llic wheel speed 
allowed to decrease. Tmmediiildy tin: liquid 



the tiieliometor reading givea the energy lust in 



in tho tnfhonietoi 1 tube reads zero the " mil, !1 

Elevation \ \ 

. i 

-H*- > \\ 



]ii'oducing fracture of the tc.sl, piece, '['ho 



Details of Hammer and Knife edges 

Km. i no. 

Hind in proved, tho knife sprinyn out and 
breaks tho lest piom Tlio iibnorptioii of 
energy fi'oni UK! llyivhool Jnwor.4 tlui HjioRd niul 



tlm " in " wind, 
(iv.) }<*r& mo tit 
M<ir.hi)ia. Tho 
iuijifidii 
nifusliinc 1 consisls 

of II hllttllHOl' of 

lOto IfiJiilogmms, 
\viiicli liafi on iin 
undorsidii a hnrtl- 
eiHid stool V- 
Hhnpcul strikor. 
Tlio t(sst piccn is 
placed hoi'i/.i in- 
on knife 
liaving a 
gap of 21 nun., 
HO that whon MIG 
lianiiiior falls from 
11 height of 4 
nictrea the atriltcr 
liits it midway 
between. Uio Hii]i- 
jiorta and oxtuslly 
t)])poilo to tlio 



.Immodiatoly 
af I IT tho blow of 
tho striker tho uiulcimdo of (ho liainniw, which 




then only pnssossos tho energy not almorbcd 
by tho test piece, atrikes ngaiti.st an anvil 
carrying hvo Jiniisinga provided with temporal 



ELASTKJ CONSTANTS 



stool Bprings. Tho springs yield undef tho 
Mow of lh hammor and rcinHtor by their do- 
llciiLimi the Piiorgy remaining in tho apparatus. 

Knowing Lho initial ouorfty of the hammer, 
this energy absorbed in frauturo of tho tost 
pirn; is found l>y taking Lho difference. 

(v.) 'I'lie. A>nxi<'.r 7S-kilo<jr<titimetrR I'c.nduhim 
Iwpttrl Te.t(ht(j jl/m:A<'c. This mmiluno is on 
tho Hiirne prinoiplo us tlio CSmrpy nificliinc, but 
sumo of 1-1 10 details uro slightly different. 

Tlio pendulum is held iij) l>y a hook uLtnchcd 
to a ropii which ia wound round a windlass. 
Tlio tup in released, by delfti'liing the hook liy 
imtann of a Hjiotsitd rclojisic, and fulling Ircoly 
swings ii[) on tlin other Hido of (.ho inaehiiio 
haviii" hroken Lho ttwt bar. Instead of 



(101) .FUHTltKH I'AllTKSUI.AUS Ol-' N O' 

BAH TiiS'i'S. Tlio leading psirtioiilar.- 
live priiiisipiil tyjiea of uotcslied Im 
tiro as foflowst i 





Stilklim 


Stvllilim 


ryDonfM^lMno. 


Kff.M. 


MotSfe 


Clmrpy ([icniliilum) . 
Amaler (pendulum) 


30 
7(5 


3-fi 


.Fivmuiit (falling tuji) . 
tiuillwy (mtury Hip) , 


20 eir (10 

(iO 


8-Hii 
fl-Sfi 



Tho iiotclHitl I'nr li-dt i 
i a- mcHtiB of tlutuiiting ft tlangr<nia 



.1/01) 'I'liHTS ON 



C'OimiHJTLY AN]) iNL'OllliWl'I.Y HEAT-THKATED 



Miit,,,,, 


Uoiit 
Trcatnusnt. 


Limit. of I'm- 
iiortlo] in lily. 


Vldil Toint. 


Ultima tfi 
Stress, 
'ons/riq. lu, 


-Jloiiftifioii. 
I'cr cent. 


(if Aren. 
Pur cent. 


A VCTUHO 


'liar .SHI 
Ilnr SW2 


IlKiOI'l'f'Ol 


10-1 


17 -R 


/in -r> 

CM! 


28-fi 


G-I'O 
3-7 


78 -0 
0-1 


Nickel (tliromo Hlisi-l 
HUP Sill 


5L 


:M - 


<H-<> 
-Ifi -11 


fill -It 
(it) -11 


S:!! 


iil-!l 
1-1 ^ 


8-tl 


Jlur HHS 
JIar SS4 . - 


(.'fU'l'l'dt 
llHUIlTHOf, 


2(1-0 


4-I-0 
1J-3 


W-ll 


iio-i) 
^i 


07-0 
(i-1-0 


81-7 

M-H 


Niokul ohronm Htcisl L 


C'Dtruot 

IllUIHTOOt 


32-3 

;u-o 


Si 


Bft-8 


20-7 
29 -1 


08 -r 


71) -5 



C:I,AHIT TKars OK M/TKIHAUH Co.mixm.Y AMD INCOKHKCTLY 



MutoriulH. 


lli'iit 
TreiitiiHmt. 


Limit ofl'ro- 
]ifttlniill(-y. 
Tons/.Sq. In. 


Ylftkl Point. 
Tons/fiq. In. 


IJlllnisito 
Stress. 
Tons/arj. In. 


Klmiffatlon. 
l.'or coiit. 


.IMiifitJcni 
of Ami, 
1N.T cent. 


Kimr&v 
l.> 
.I'mcUirft 

KK.M. 


Uoilur iilulo . . i 


C'tiiTfiut 
Inoorrcsot 


18-3 
M-2 


10-1 
18-3 


27-9 
20 -0 


-J2-2 
31-0 


02-8 

eo-i 


c-:i5 

O-KS 


Niokololii'umoiimiil; 1 
Him ft t 


('.'nrrcol 
Inoorrcot 


27-0 
20-0 


33-0 
32-0 


45 -Z 
-14-0 


21-0 
23-5 


Si) -2 
57-0 


10-71 

2-i>7 



f bank ugfiiiv, a^i in Lho Charpy mnuhinot 
it is hold in position by a coud passing round a 
drum and acting aa a braUo. 

On falliiiR from otio side, tranavorBO (bund- 
ing) LcBtsi JUT' mado, while (ensile tests arc made 
when tho pendulum falls from the otlioi- side. 
Tlio onorgy in tho hammer before and after 
tlio test ia registered on two movable straight 
Bcalra by the movement of tho pendulum. It 
is so arranged that tho second scale raises tho 
pointer on to tho first eunlo and indicates tho 
actual energy absorbed. 



dition of nuci'ostrucLuro duo to faulty lioat 
treatment. 

The liirgo variation in tlic energy abnorlird 
in tho Izotl test duo to alteral-ion uf bout trc-iit- 
mcnt is well shown by the figures in 'l?abb :)2, 
taken from a paper by Pliiljiot. 1 

Soiuo teats by tho author on ft pioco o 
boiler plato and nickel chromo crank shaft nra 
piven in Table 33, -and abow tho same ]dnd 
oE variability with ht?ftt trcatmnnt. 

1 " Sonio Espcriiuents on WotuhctV Hurs," lititt. 
of Automobile tiny. 1'roc., April 1018, 



206 



ELASTIC CONSTANTS 



Wild has shown that the brittloncs 

in steel resulting from a high pcrcontago oi 

sulphur and ])hosphoriis is well marked bj 

tlie iKod lest. .Hi; says, " Certain steel fo'i 

innldiij* nuts and bultn was found to contain 

sulphur and phosphorus in excess of (H pei 

cent; such ated invariably failed to give any 

higher reading than 2 to :i ft.-lb. on the Txofi, 

whereas a steel of exactly similar composition 

and with similar treatment but with sulphur 

and phosphorus below O0(i per cent gave an 

IKOI! lent figure of over -10 ft.-lI)H." 
S (102) .DIMENSIONS ou STANOAHD TKST 

PIECES. Although there arc sovcral impact 

taiters in Britain of tho .I'Vemont and Guillery 

type, tho majority of tJio test houses HHO 

I'/tui or C'harpy machines. The dimensions 

of test pieeeu for these, machines IHITO beon 
standardised and are shown in ./'V;/. }'2{). It 
will bo noted tluit in each n-, W o tho cruss- 
soctional dimensions arc 10 x 10 mm. and that 
the form of notch is tlio same (tho (Juillery 
niacJiinc lines the same wi/o of test pieees as 
Uio Oharpy machine, while tho JWmout test 
pieco is smaller and ia described in (98). 
Tho form of notch selected, and sometimes 
called the- I/.ud notch, in a 4fi vec, 2 mm. 
(leoji, with ft root radius of 0-25 mm. 

(103) TUB ANGLE ov TIIK NOTCH. -Ex- 
periments by Thomas 1 at the Watcrtown 
Arsenal show that, with mild uleo), tho angle 
of tho notoh dons not appreciably affect the 
results until it has exceeded 45, The results 
that Thomas obtained are given in Table .'34. 

(104) HOOT RADIUS ANU DKITII OF No-ran. 
'fho ]0x lO.mm. test ]iieco in which the 
notch ia formed by a drilled holo 1'- mm. 

a'Aiii.i; .'14 
KiTi:f!T OF VABIATIOH ob- ANCH.I: OP NOTCH ON TIIK KNKR (I V , 



The shape nl tho bottom of M, n*^'^ 1 
an important effect on the work l>.Ht'H )l '< 
fracture, whioh has it H \ ma t Vlt ] nn ^vhtni 
anjrlo at the bottom of the notch IH *** Jlt '' 
zero tut possible, 

.Results by I)i.\, 2 summariHorl iti 'l*n.i>I'- 

and by the author (Table Sfj) show f-.liin <''' 
very flearJy. 

TAm.i'j ;i5 

KVVKIIT or HAiinra AT TIIK Hnrroni ai? n-t i !: >'> 

, ox TIIK KNKHOY Aii.soumin J N FitA^ri'i' n 1-3 

Niokol cliroino sled rod, j" in <Haiiii^t.i*r 



Form nf rTolcb, 



2 mm. (Jncji (4fi vcc)Hhnrp 
2mm.dc|i (<ir>" vt'(s) 0'1'fJ | 

nun, rout nidiiiH j 

2 mm, dc!p]>( parallel sides) \ 

I mm. roof, mdius ) 



Il 



Jj't.-lb.t. 



20-0 



40-3 



'i'Aitr.n 36 
O-CfiiHsrccnloHrboiiBtccl, vco notolics, 2 mrtt. 



Hoot 


Itadiiw (if iViiteli 
it) iniu, 


(Char 






Ft,,ll,, 




l.r|i 


4-05 




0-17 


C-8G 




O'H'l 


8-.1I 




0-08 


13-7 



in 



(Oharpy ftl.-ic-] 1 1 Jii>>, 



o-jir. 
i - 1 ft 

1 !> 





C'h 


iriiy ImiMHit Viilurs. 


AllJilfl of Wnfrli, 


l''1-.-llw.7K(). .In. 




-llaxliuuin. 


Jlliihiiuiii. 


Avoratto 





304 


2(10 


28/i 


15 


340 


283 


aio 


ao 


323 


281 


21)8 


45 


382 


801 


3!)4 


CO 


071 


CIO 




7fl 


800 


818 


854 


111) 


830 


800 


814 



diomotor, proposed by tho International 
Association of Testing Materials, cannot bo 
produced economically un the majority of 
nlloy steels. 

TJio form of notch selected as n standard, 
viz. 45" vco notch, 2 mm. deep and 0-2o mm. 
root mdius, duos not milrer from tins objection 
ii8 it can bo easily produced evon on tho 



Aii|{tn of 'liiijid. 
J)grcfis. 


liritti'I 


lfi-8 
15-2 


70 

77 


i/i'O 


81 


arj.jj 


SO 


fid-2 


RO 


130 


va 


130 


78 



JMr.. 



ny Imrmct Tosts on Ifnat-'l'mitcd Htcels " 
'(. jl/(. /'roc,, 11)10, sv, 75, 



It has been found that the sharper tho 
is made, tho bettor tlm tost discsriin 
between brittle and tough materials, 
to say, that as the material tested 1>ocr< 
toiighm- the cA'eot of all oration of iho 
ratlins is loss. 

It is unsatisfactory, oummoromlly, it* . 

ardiso a dead sbarp notch as it is (1 iffi emit 

3 " KiiiRlo Blow Notched Ear Impact Toad a rm>il 
In tho Amorlmn Iiimistiy," Amer. Xoo. y'cst ' 
1'roc,, 1019, xix. part II. 731. 



ELASTIC CONSTANTS 



207 



in lio always mire llmt it in produced. A rout 
radius of. O i 2. r ) linn, lias beon wlrehsd sis it is 
found that, \villi !i radius of this siiw, tho lest 
ia still isfl'eclivo in thu detection nl faulty heat 
treatment. 

It has also bcon found tlmt shallow notches 
iiierenso the enorfiy tn fraclnru {>f tough 
matoriuls relatively to that rcfp.iir.ed fur hritllu 
inateri.'ilH. 

(105) SJIAI-K (W TEST Pnsou. Philpol ' 
found Ih.'ita round fcst pieeo can ho produced 
wliiuh can he used for acceptance testa on 
hen I -treated steels in plnco of the standard 
Bijiiiii'o apeoinien. The Ifillnr is, however, far 
tlia more desirable from the point of view nf 
testing find, by properly rigging up fur tpian- 
tity production, it can bo prepared liy a pair 
of straddle mills just ay economically us the 
round le.st piece. 

jj (100) COMI'AHIKON OF TuSTS ON DlFFKIUONT 
]']iil|)it a IMS mudo n cm|)arison 



ON 



lest [lira 1 -, notch, distance brtwi 
find rudii uf suji|iorUi and Htrikor 
utiifiniii. 

5 (107) EKPIMJT OF 
Tin-; KNHKGY TO FuAOTimi-;. Bulb 
ami .Fremont haw found a. variation of the 
onergy absorbed in fracture wilk HtrJliinj^ 
velueity Ijnt in opposite- directions. (Jliurjiy 
lias fount! tlmt Iho influenro of the rato of 
impact is praclienlly ineligible within limit;-] 
which do ])i>t oxcuucl lliiiao of appliances g^iior- 
ally einjiluyetl in tbo Irsling liihtiraltiry. 

Some thesis carried out by tins mithor filiow 
Ihfil, on a inaehiiHv of Ihe Olinrpy typo at 
sinking velocities np to 411 ft. pur second, 
increasing sinking velocity may cither inoreiiao, 
(leerease or unallor tho energy abnorlmd in 
fracture according lo tho inatoriul iip'.m whieh 
the testa uro made. Fu any cams tho on\n;l in 
not apjin.'oialile until after a- velocity ot Hi ft, 
per Bets, in rauehed, ns in shinvn by tho resullH 
of tests in the Chnrpy (beam) and l./.ott (eanti- in Table S7. 

TAHM-! ;t7 
EFFECT OF STKIKISO VIILOIJITV OM THIS Ksmmr AIIHOUIIKD IN I'n.ici'uiu; 





'Kni'i'iiy nlworliwl In I'nicturt 1 . 


HI.HtdtiK Vi'lnrily. 


Matorhil. 


KB.M. 


l''t.-11lH. 


ftftitrrs/Hrr,. 


l'','i-t/Si'i=. 




!( 


asi-i 


2-7 


S) 




s-m 


27'7 


1-!) 


III 


Mild hlucl 


^77 


2(1-0 


(!! 


HI) 




2-(lll 


1'1-r. 


8-H 


I'll 




a () 


2-I> 


'!! 


lit 


.Iron ... 


2 'HO 


20 -2 


l!-t) 


21.1 




1-17 


KM) 


j;t>i 


'13 




1-00 


28 -ft 


2-7 


1) 


Nickel oliromo atecl . 


4-10 


31-8 


'1-0 


Ifl 




B14 


;)!);; 


KM 


Jit 


| 


1-OS 


7-fi 


2-7 





Medium carbon atcul . 


1-05 


7'(J 


(H 


L'O 




1-05 


7-0 


18-1 


4 



lover) maoliintis on tbo atandnrd lOxlO-nim. 
test pict-o with thu 45 sliindnrcl notch, 2 mm. 
deep and O'Sfi nun. root radius, >lo finds 
that, wlioro tbo eiint'gy abntJi'liiHl is }o&s than 
70 ft.-lhs., ntiUsliecl bar toslrt, inado in cither 
the Charpy or tho laod maeliincs, fjive similar 
values, but where tho cnui'Ky absorbed in 
fiaoturo is Creator than 70 ft.-llw., thero in a 
tendency for tho values -from thu Charpy 
machine to bo somewhat higher. 

Charpy ami ("ornu Tinman.! p liavo nmdo a 
series of experiments, with a steol 
projmrcd togivecoiiHistent icsiills, on " Ijo 
innohinca of throe different tyjiert 
vortical drop, and rotary) and havo found 
tlmt, in regard to energy absorbed in fracture, 
tho results arc practically identical when tho 

1 " Some Mxiiorlincnts on JTotdhntl llnrH," Insl, 
oj Automobile Hug, Proa,, April loifi, 

* lliiii. 

3 "Now Hxpocimnnla on Hhock Testa, " Iron mid 
Steel Insl. ,/ourn. No. 2, 1.017, ji, 01. 



(108) SLOW HIJNIHNU Tv,ivr ONT 

S. It haa hcon shown by I'hilpot l jincl 
others that, if it nntcliod luir lest pioco I'H 
In'filcen slowly, t-hc work expcmlecl is ijoni- 
jianihlo vi-itli tlitit ineaHiired by an ini]ui<:[i 
inaohitHifatnuidfiTatoly low striking 
mid is cr[ually n cfleofivo in 
between coi'tain biittlo and timyh 

As an avonigo of a largo number of 
i'hilpot found that tho enorj-y aluiorbod in 
iho slow bonding tost in iibnuL 7/5 ]IKV nt nf 
that given by an impatst lest (in two or tbrcn 
cases tho cnergioa olilivimvl l>y tho two 
]iiothod9 nro approximately (ugiial 
JittrihiitoH this dift'eronoo to enoi^y 
in the pniiiluluni tdsi.ing macliini?. Tho strik- 
ing velofifcy in Philpot's impact tcstH did 
not cx(iec!il 3-5 metres pur fieramd, and bin 
conclusions only hold up to Hint 

Philpot. for liin s\iiw beiuliiij,' 
ordinary Brinoll iniiolune, ami monsurcn Ihn 



imtl 



203 



ELASTIC CONSTANTS 



H of tho sipmmcm for different loada 
by iiuiana of 11 microscope. Tho results nro 
plotted and the area nf Ihn curve is integrated 
in order to olilidii tlio total energy absorbed. 
The. Hump/inn Aulwjraphia Notched Bar 
Tilling Mnefiiat, made by tho Foster Tnstru- 
mont (Company nf Lof/oh worth, IH dovisod to 
cany out this class of lest rapidly itnd con- 




voniontly and in a manner giving the maxi- 
nmni information as to tho material in a 
minimum lime. It is illustrated diagram- 
mutically in Fig. IW2, and photographically in 
ffig. 1M. 

Tho tost piece A in gripped in tlio vico 
31, so that tlio jaws tit tho vico aro in lino 
with tho notch in tho test piere. Tlie socket 
is (iltiichcd on tho projecting end of tho 




Era. 133. 

tflfit piece, and is a reasonably close lib thoroon. 
A bending stress ia applied in tiio teat pieco 
hy moans of tho winch 1) and the wire E, 
wliidi i attached to the outer end of. tho apring 
liar .I 1 '. Tlio inner end of the spring bar ia 
firmly fixed to tho sonlcet C, Tho outov end 
of Mm spring har is supported by two rollers 
<i and C'j. Tho Honket (.' carries also a rigid 
bar M. 

The deflection of tho spring har F is a 
measure of fclie bonding moment applied to 
Ihu test piece. Since tho rigid bar H ia 



not subjected to any bending in 0111 "" 1 ' ''' 
will move through tho same iinplci * '""' M0i: '"' 1 ' 
0, and this movemoiit will "tho r of'* 1 ' '!" (L 
mcfiKiirc of the bending of the t^'- 1 * 1 ' I 111 ''' 11 '' 
The pen J slides ujion tho ngul 'l l -|" El - n l(s 
position being dotorniiued by Uio thin ivii'i'.'i 
or cords K and L, which aro kcij*^ lu "'' ! !- v , a 
light spring SI. One end o f thf ^virtJ^ K IH 
attached to a jioat. N so that as l-li'.* i''^ 1 ' '""' 
II moves in eoiiHequonco of tlio Ij^nditLLr nf 
the test pioco, tlio wire K will (lr*f%v' tli" [n-u 
to the right. The point of \-\\v ] <-<ti ]imrlin 
U]ion a calibrated chart P pnt'r't** 1 ' " II ' ^ l(! 
spring har ]>', therefore, if Hit) tc:Ht |iicc(i 
offers no rcsintaiu;o whatever *-** Iji'inlin;; 
force tho pon would draw a horii" ininl linn 
on tho chart, the length of whin It i" 1 IH'-M/ 01 '- 
tiimal to the angles through which * ho U'st jiicro 
is bent. As, however, tlio lost pic-tst* fl*'< i .s 
resistance to bonding there will bo "- J'C'.Hn 
movomcnt between the spring bin.' I 1 ' u " 1 ' '''"' 
rigid bar M. 

The pen, thcroEore, clniAvs a dinyrin'n wliDwinj^ 
tho relation between bending JHOJUCMI I. iippl^d 
and angle of Ijcnding throughout l:-lm* <lin'iilitni 
of tho te.it. Tho toLnl cnoi-gy ii,lMorln'il in 
tlio breaking of tlio teat pieco ciiti l>t> tilitiiiun'tl 
from the urea of this) diagram. 

Tho maohino oau also E)o Htic^tl wilh nn 
integrating device HO tlmt tho rtuirj^.V rUiHorfn-d 
can ho read dirootly from tho inuclii'"*- Thin 
device ia shown in .Fitjs, 1I-J2-3. r ]*ln' wii'o K. 
jiiisiseH round a ptdloy Q. '['Jii! jmlli^.v (,J lit 
attached to n spindle Jitiviug at iis^ Itj^viir cud 
a friction disc K, so tliat tho hoiii-li n^; <>T tlm 
test picco which resnlta in the movement nf 
the pen to the right also results iti. 11- JH'OJHII*. 
tionato rotation of the Motion dints -I't. 

The iimler face of this dUo roMts-* ii]nu llut 
edge of tho friction wheel, not HJo%vn. Tim 
spindlo of tlio friction wheel ia isivi'i - ii'(l \vil.li 
tho obart plate upon tho spri i XJL^ hur I 1 ', 
When tlio bunding moment in xoru (-lio friolirni 
wlicol is afc tho centre of tho friction dine, 
but as bending moment ia a])j>Iic;cl, tiTiil (horn 
ia rotative movement botwcuu l-lit^ H|fHnj.( 
bar j.' 1 and the rigid bar H, tl jm frii.il inn 
whool travels towards tho ciremii fort n LI 'ti nf 
the friction disc, and is conscquoiitl^v voliiti-fl. 
The rotation will ho proportional tn i.lio |ji-odnnt 
of tho bending moment applied and Um H)i|.;lo 
of bending of tho tost pioco, niifl MIIH <liiviro 
will tlioreforo integrato tlic 
absorbed in breaking tho teat pic. 
upon tho outer end of tho spmcllo 
tho friction ivhcol is an index liters S ^vhioli ran 
bo calibrated to read direct in ft.-ltwj. 

(109) TESTS am SPECIMENS Ok- .'I >IKI.'I-;IH':ST 
SIZES. A trustworthy relation IUIH. not I'IMI 
found between tho energy to fra(ii:ni-ti in lent 
jiieces of different sixea; thci'o JR., liownvc-c, 
evidence thnt it ia ])rol)ably tltJYVinmt i^ri 
different matorinls. This ia shuwji Jfnim it it 



ELASTIC) CONSTANTS 



ion <if the rtismlLa in Table !W, which 
(jrivi'.s tlio results of iiiiiolicd bur impact teats 
on two dilToront stools with geometrically 
Biiiiilur lent pieces. 



given the ductility in the names IcniiH nx the 
static ' tciiBilo test, namely, ]oniiUon inul 
(ion tractitin of area, but iilw'jiys with highi'r 
numerical values. Tho brealdiii* tslresn of 









Knr-il'y tt 


Pnu-U,. 






r>f Kiu-cliuiHi 




Stool A. 






Kli-i-1 1!. 




















KK.M. 


KK.M./L-IU.'. 


Kg.Jt./Oiii. 3 . 


KK.M. 


KK.31./H.L..'. 


ICtt.MjCi...', 
















:n> x 30 x i oo 


CO 


8-33 


042 


3G., 1 ! 


0'IW 


U-^G 


O 3 xo:>x 3 :.e 


m 


n.32 


0.2, 


107 


20 


0-lfi 



' Tim notch for Uui Klx 10 teat iiic was n -li'i" vcn, 
not(!]irt fur tins lui'Kor tot pkuiss ivero BtsoiLictrlually nhnllnr. 



IHIH. runt riKllut) inul 2, iniii. ili-oji. Tliu 



It will 1)0 noted tlmt : 

{I) Tlio (morgy absorbed in not proportional 
to cither UK; squaro or tho oubo of tlici (Union- 
fiiiiiis of the leal piece. 

(2) With tho 10 x LO-nnn, toat picoo, stcol A 
tiilccs 3} (.inifift tho omsrgy that Blecl Ji docs, 
Lilt with tho OS x OD-inin. teat piocoa it ia only 
1A tiinc-s. 

'riioro is nppurcnlly a HOiilo s]ie(!(l fnctor 
in tho law of rcssiatantio ot imlolietl HpommoiiH 
to Hiiildoii shook which apponra to he of 
oxtrdino eumploxity. 

(1 10) '.DKS'i'H LIN UNNOTCIIUD JUus. With 
goomotrioally similar imiiDtuhod tost Uars, 
oitlun- lioaniH or tonsilo tcHt yioisca, tho energy 
in fmoturo for tho ainno nmUsi'itil if) 
to tlio volume of tho teat pioco. 

lintl-, 1 in 190*, na tho result of Homo 
oxporimoiita in dynarniu Letinion, eaino to tho 
communion tbnt, for stools, thoro is littlo 
(lilYnrciico in Llio total elongation and tho 
Tinib work in fmoturo whether the fracture 
is brought about in 10 miiiutos or O'Ol aooontla. 
Slanton and Bairatuw a in 100S and Deliklmw a 
in 1900 (using a drop liamnior typo of nmohino) 
ho-ve also shown that tho tonsilo imnaot test 
(i.t. dynaniio tonailo teat) yivos mimorioal 
vnlttos which agroo with tho rcHUlta of tho 
Btntio l;onsilo tost. 

Blount, Kirkaldy, niul Siinkcy, 4 in tho 
summary to llieir papor on stool tenting 
methods, sav that " tho impact tonailo test 



'J-'anl. 



11101). 



Test 
Vest. 



ami 

lust. 



Tmimcfc ToaU of Slotals," Amcr. Soe. 
t\lal. 1'roo,, 100-1, Iv. 28S, 
' UcBlBtanco of Matorlnto to Iinpaot." IiiRt. Meclt, 
I'roc., Nov. 20, 100B, mid Jtetnte tie AlMall,, Jfnrcli 

1 Nol:o on tlin .Rnpluro of Normal Cylindrlrnl 
HnmiJloB l)y r,ans!tudinnl Imimut," Inter. Assoo. 
Mul. Ptae. t 1001). 

' Ooiii]inrlson of Um Toiiflllcs, Iinpnrt Tcnslln. 
lloiioatod Bniiillng Jlotliitds nf 'JJcatluu Steel,' 
Aleeh. Huff. 1'roe., 1010, Jlay 27. 

VOL, I 



tho material can lie inferred, but must Im 
foduee-d by a factor in ordrsi 1 to obtain Ihn 
Name numerical value us givisn by Iho tntiu 
tc-Ht ; also it only yivi-n tlics I (milting HLro.s, 
Tho onorgy absorlKst.) jinr cubic inoh d(;H nut 
vary greatly with the various tyjiea o[ aliiclj 
it EH a|)|)roxiniately fit) per cent nn>ro tlmn 
that obtiunod by tlio aliiliu lonnile lest, tint I 
is n!so no elofinito nriterion of tins lyjws of tlm 
steol ; at any rale, of mirrnal ntnela Linnlaiiiinj; 
a Biuivll pmpnrliun of ])liosi>luiru.H, From tin- 
exiJoriincnl-H I'flforrtsil to by Breuii & it would 
appear that Hlccis conlitiiiiiiff an unduo 
|)oi-tion if pkoaphonia gives a inuoh 
energy per cubio iiusli witli iuipact 
teslH," 

g(lll) TESTS IIMDUII .HiirnATun B 
IMPACT. In 1903 Stan ton puri'ied out ox- 
tonflivo investigation a on tho method of twHng 
hy repeated impact, and devised a nmohhio In 
I'oprodueo stress eonditiona which aro met wJMi 
in certain machine parts in notunl use, wluuxi 
tlio effect of alternating blows is produced 
n the material at poflitioua whom lhm i)i 
a vnpitl rediuition of croHS-aooMon. Tho Icjil, 
bar, O'fiOO inch ditimotei 1 nnd (f-5 inchca hing, 
ia Biipjioi'tccl on knife edges 4^- inches apart, 
'I'lit! teat piece has a groovo turned round tho 
(iciitro of the apun O'Of) inch deep, HO 1-hn.t Ihn 
ofl'uotivc diiimetor at Iho bottom of tlm grnovii 
is 0-400 inck. Tho groove it) in tlm form of 
a veo, whoso unglo is fi5 nnd mot nidiim 
O'Ol inch. Tho tnat jiioeo ia fixed in Ibo 
machine, where it receives blown (it tho ruin 
of about 00 por minute from n, bnmincr wlp(> 
weight in 4-71 Iba., nnd of which tho height 
of fall is fuljimtable. 



, 

' " Rcshtanco of MutCTliil* to Imiinnt," In at. lUi'ffi, 
]ltifj.l'roa.,Nov. 20, 1008, unU Heine demtlall., March 
1000. 



210 



ELASTIC CONSTANTS 



Between each blow the bur is turned through 
180 and tho test is continued until failure 
of the test bar. Tlic number of blows to 
cause failure is recorded by a counter. 

A scries of teats w usually made on each 
material with varying energies of blow, and, 
by plotting the energies of blow ua ordinntes 
ami the number of blows to fnicturo as ab- 
acisaio, a curve is obtained from which useful 
information as lo both the impact strength 
and fatiguo strength of Iho matorial can bo 
obtained! In Stallion's original paper it is 
clearly stated that when Uio luimbor of blows 
is less than fiOO tlio results approximate to 
those of the single blow impact teat, and that, 
when tho number of blows for fracture exceed 
100,000, tho results arc in the order of the 
fatigue ranges of the millennia as determined 
in a Wolilor lest. During tho war it has bi;on 
a common practice to compare materials by 
the number of blows required to cause fracture 
when tho height of tho fall of tho tup in kept 
constant. As tho height of fall selected causes 




1OOO SOOO 3000 400 O GQQO OOOO 

Number of Blows to causa Falluro 
FlQ. 134. 

fracture after from 4000 to 0000 blows tho 
results cannot bo properly interpreted. 

Tho results from tests on steel correctly 
and incorrectly heat-treated are given in 
Table 30 and plotted in Pit], 134. It will bo 
noted that tho incorrectly hoat-trcaled bars 
are considerably weaker as regards notched 
bar impact, but slightly stronger under fatiguo. 

TAHM-: 30 
Hui'EATHi) BENDING IMPACT TESTS ON HOH.ER I'I,ATB 

CORRECTLY AND INCOUHHCTI.Y IlK AT -TREATED 



ICiiCTKy of 
Hlow. 
Imrh-lba. 


Nnmbor of IHowH lo CMisa failure. 


i\ tote rial correctly 
Heat-tronleil. 


Material incorrectly 
Jlcat-treatotl. 


3-fi3 


3880 


C871 


tf-71 


2330 


2913 


fi-80 


103C 


1450 


7-35 


10.1,1 


620 


13-32 


47.1 


250 


2-1-1(1 


155 


Gl 


The test bar previously described ia the one 
adopted by fitmitoii for his resoaroli, and has 



a notch very similar to the standard I/ocl 
notch, M'hieh is easily reproduced. A notch 
0-05 inch wide and 0-Ofi inch deep with 
parallel sides mid practically sharp corners 
has boon sometimes used in eon junction with 
(.liia tnst. 

Tho 1 'Id en- Foster machine, manufactured 
by the .Foster Instrument Company, .Letch- 
worth, is a close copy of Stanlon'H original 
machine and embodies its! principal features. 

Tho illustration (/''/'/ I'l'') k'i v(1 - 4 a general 
idea of tlio external appeanuiee of the machine. 
Tho main Hpindle, not .shown in the illustration, 
projects through tho nido of tlio box canting, 
and is driven by an electric motor with 




I'm. I3fi. 

Hiiitable gear or worm reduction. About 
04 horse - power in required to drive tho 
apparatus, 

Tho main spindlo nari'ies a dog clutoli 
driving a cam, which has a roller bearing en 
its upper surface and attached to tlio lower 
end of the rod II. Fixed on the rod II id nil 
arm J" which engages with the lower face of 
tho hammer M ; thus, when Iho rod IT Hues 
by rotation of tho cam, tho hammer M is 
lifted. Tim guides for the hammer consist 
of two sets of three point screws carried by 
two castings attached to the standard 
and its follow on the opponitii side, 

Mounted on tho standard ('} in, a olcovo 
W, free to rotate about the Ktandard, hut 
normally held m a fixed jumilinn by a spring 
L. Clamped on tlio sleeve W ia nn adjust- 



KLASTTC CONSTANTS 



211 



nblo Rattdi K. AH Komi aa tho ai.'in J has 
liftud tlic luinnnor Biillieiimlly, tho spring L 
cittifioa n partial rotation of the ulnevo W, 
HO that, wlioit tho nrin J again descends, iho 
hammer is hold by the- catch K. The 
further dcscnnl of tlio arm J brings its lower 
imslinod faee in onfia^enifiiit with the roller 
N, attached to tho hloovo W, in sueli a 
man nor that tlio catch .K releases tho 
hammer M, allowing it to full upon tho 
test picoo 0. Tho liamwor M is furnished 
with n hardened tool-steel tup. Two hammers 
arc provided to allow for a wide range- of 
teals, tho -weights boiii^ 5 and 2 Ihs. roHpeot- 
ivcly, Tho height of drop, which depends 
upon tliP position of tho adjn.itiiblo catch K 
nil tho slccvo \V, mm ho varied from 1 to 
4&- inches. 

Tlio test piono is earned liy two hardened 
stcul luifiliKH in tho |)luninuu' block PI*. It m 
rotated through 180 between muscossivo bhnra, 
tho rotation licing arranged so that it begins 
and ondf* entirely between tlio puecessivis 
blows. 

Tlio revolutions of tho teat pieco am 
rct!frtlccl by n tiounti;! 1 V, ami llio niunhor of 
blinvB is found liy ninltijilying tho noiiiitot 1 
record liy two, Whon tho test piece liroaltn, 
it on int'S in conliiot with an arm X, anil 
thoi'cdry trips the diiluli ami alojis llio 
inaolnno. 

Tho fcrat ]iiij(jo in driven, through a, nnivoi'Hiil 
join!;, by tlio uhain S, friio. wheel and clnleh 
T. Ono end of tlio uhaiii IH attached to tho 
rollm 1 , ill; thn lowor end of the rod II, wliieli 
buai-H, ttn tlio cam, and tlio other end darrioH n 
suitably guktoil weight. 

All tho gear is lived to the casting which 
forniH llui cover of the lower tank casting. 
Tfii! lattiu- ia jiartiiilly lillod ivil-h oil for 
lubrication of tho fliirfauus. 

(112) Kpls'KUT OF TKaiL'MHATlWK ON TH1J 

MRtHiANiciAt, rittn'iaiTiES oh' ft I UTAL8. Many 
parts of 'machinery work at lom|U)r.lm'ca con- 
skloiubly uhovo or below tho normal, and it 
if) osfKmthU for tho jiiirpoHO of economy and 
Rafoty in design that tho more important 
oileotB of tompnraUiro on tho meohixiiittal 
proportion rif matoriola nlionld ho well under- 
stand. 

(11 3) TKSTINO AITAKATU.H. Tho oldost 
motliocl nsocl for testing at temperatures abuvo 
(hut of tlio ait 1 was that of floating tho tost 
piece in a furnace, transferring it to tho tofttiiiR 
niacliino, and conducting tlio twtt very quickly 
in ivii 1 . Tlio valncii obtained by that method 
woi'O very imroliahloj and in rounnt tests tho 
Bftinplos havo been immorflftd in ft hot bntli 
for tho whole duration of tho test. 

Tho medium HRcd in tho hot bnth enn oithor 
bo a liquid or gaa, but it is essential that tho 
heating medium Bhoiikl neither attack nor 
alloy with tho test piece. Suitable materials 



for liquid baths aro {.nvon in (ho tollowi 
iable : 


Jilufci'ial. 


TttmiuM'iiliire used 


Wntrr .... 
I'araflia .... 

Nitrate of jmUHsiurn mid) 
iiitrnli) of sodium / 
Lead UIK! tin 


U]i tfi Iflfl 

UP t<i aofi 
Up to :t.w 

3f)0-GOD 
300--IOO 



Air in nearly always iiHtsd for the pas bath, 
but it onuses oxidation of the lest sample, 
and for H pedal OIISPH I ho test may bo cjarri^d 
out in virctia, 1 uitrojfon, 3 or carbon dioxiiJo. 3 
lludoluiV ' made MHO of Imtlis of filoain (up 
to 100 C,}, naiflithnlenc vapoui' {^OO (X), and 
naplilbylniniiio vapour (!H10 C.). 

T.ho heating of llio balli in aaniwl out in 
Ri-voral ways ; 

{]) liy gaa jota an-ntigcd undorneatb tlio 
test, pioccs, wluoh ifi Imhl hon/ontnl. .ThiH 
method is adopted by Unwin & for a- liquid 
hath, imd by t,lhin-]iy fl for an nir hatli. 

(2) liy gns jn Is above a horixoiitnl lest ]>ioo(! 
ailo]ilod by l,n Chiitrliet 1 . 7 



iu noiijiinotiim wilb a 
liy Marions 8 and 



testing 



on fiO-fi'ot l(>ngibn of copper wire, up to 
l(n|]nratrofi of <iO" ('., cni']'ied out lit tbii 
Kaliinial ["liynleal J.abi.L'utoi'y. 111 

(5) lOloiiirii! henling eniln nro us<*I by 
Ktriheeli, 11 and Mopkiimon and Angora." 1 

l''or ^RiiiM'iil eonvonioni'e tlio last niolhod 
i.i to ho profiHTiid. '.E'wn t>li!tttri 
ouccOHsfully nsi;d at llus National 
Laboi'Jitory, arc given in Finn. I'M mid_ 1M7. 
Tlioy tiro both uml in cimnootion with a 
vertical testing maohino. 

A platinum funmco for UJinporaturcs up to 
1200" 0, in shown in Fiy. 13(1, Tho lioiit<ir(a) 
consists of a platinum strip, 1MB" x 0-0007", 
wmnul oil a firo-cslay uylinder (mitaidn dmmtilcr 
2-2j> inchcfi, t!ii(Jtncsa 0-JH7 inch, and 1SJ 
inches long), with n pittsli of 1 indi. Tho 

1 Hoaenliidn and ]lnmi>hroy, Iron unit Kiwi Intt. 
J,, JIH3, No. 1. t 

' Ildjikhison nntl llnRors, Ilngwfcniifi, llillfi, 11. 
331. 

3 nicnROUKll nnil IIiuiHOii, Just, f>f MettthJ., 101-1. 

I Alill, (t. tl. Kgl. Ti'din, V trsufhrnmlHlifn ztt 
lli-rUn, 1809, l>. 292. 

' "U'lin StrenaWi (if Alloys ab PLfTimnt 'LonniiTH- 
tiiroK." Ilr.iiortaf llrii. Awnc., I81>0, . 

Jlitllfttii ile In WMiVM tl'cmourtiftcmfnt, 1H1H). 

' JJattmntcriallttiiittc, 1001. p. lf>7. 

8 Milt. rt. d. Kal. Tce/ni. Pfrsnehsaiistaaen ztt 
llcrlin, .1800. 

Kfils. \'rreiitrn }>i-iit.Mh, Inn., ]fln(),p, 17-11); 1001. 
pp. 1(18 and 1-177; 1003, p. 1702 ; HUM, 1>]X SUf. anil 

' 1D ']lntann, "Hani-drawn Copjiui Wlro," C'oltccleil 
Researches, S.P.I,.. :hHB, vill. 

II %e.itx. Verciae.it Deulscli. Ing., IU03, p. 560. 
" Knyinctriw, 10B5, H. 331. 



212 



EL AST [0 CONSTANTS 



ends of the strip aro clumped in position 01 
tho cylinder by meliil clips |). A nteel case 
Jl (about 8 inches diameter and 1/10 inch 

Fimmcc liuHafrani i) thick) SUlTOUnds the 
Testing Machine heater, ami tllC Space 



flic fill CluiapiiXJ Strip 
(DL 



PMtnani Strip - 

(0.75"xQ.OOt!7" 

I" pitch) 




Diagram Eticnvlnjj 
nielli oil of winding 
UIG Platinum Str 
on tha Hen. tor, 



Sectional Elevation 




tine Ion on lino A-U. 
Fill. -liiO. 



between tho two is 
packed with asbestos 
and magnesia fluff. 
Tho whole is clamped 
between two end 
plates (j t and C' a , on 
one of which two 
insulated terminals 
aro fixed ; those aro 
connooted to the two 
cnda of tho platinum 
heating coil, Tho 
furnaco, which ia 
slung from tho top 
shackle of tho leafing machine, takes a ourront 
of 1/5 amperes. 

Fig. 337 shows tho 000 0. furnaco. With 
thin furnace- tlio heater is fonnod with ni- 
ohromo wire wound on to a brass tube A 
(2jj inches diameter and 15 inches long). 
The tube in bound with niioa, before winding 
tlm wire, in order to insulate it, and over 
tho wire a binding of asbcatoa string is planed 
so as to keep tho former in position when if 
expands on rise of tomporaturo, Tho boater 
is Bill-rounded by a sleol caao B, 7 inches 
didinotor, and the apaco between tho two 
is filled with asbestos fluff. Two stool plates 
D! and C 3 aro I>olted together, clamping the 
heater and outer ease between thorn, and arc 
arranged to connect tho furnaco to tho frame 
of the testing machine at E t and E 2 . Tho 
enda of the heating coil aro connocfcd to two 
ted locmmala on the top pin to. IS r o. 18 
-" wire, Iiitving a carrviiif? capacity 
"" at fiOO (!., is used fur tho hoator. 
!l "'l cloflcr afc tho ends, in order 



to allow for tho conduction of heat through 
the shackles and givo uniform heating ovor 
tho central 3 inches to 4 inches of the furnaco. 

Li another furnace of the same type tho 
conduction of heat through the shacklec SH 
equalised by having tho main healing coil 
wound at constant pilch throughout its length, 
and supplementing this by two further coils* 
one wound at each end of tho furnace. Theso 
coils aro wound over the main coil, mica in- 
sulation being inserted, and aro connected to 
separate circuits. 

(114) AHHANOHMUMT ov THSTI NCI-MAM UN]'] 
GRIPS AUD liAl'M OF LfumNfi.-- It, is important 
that tho size of test pieeo, foi-m of gripa, and 
Jength of furnaco should he carefully propor- 
tioned to obtain uniform heating of the test 
piece. Itisfoiind tlmtoitherhigh chromium low 
carbon or high tungsten high carbon steels (i.e. 
13 per cent 
chromium, 

0-30 pOl'COllt Insulated I'e 





(A) 




tube ivaunil with 
Hi-Chrome wlre.Wlreil 
oloaer at tint ends to 
allow far conciliation 
HID shaatttw 

carbon or 18 
p o r cent 



t li :z2zl?f 



'/Mail Insulation 
on tho Uraas Tube 

Sectional Elevation 



tungsten, OG 

per cent car- 

bon), give tho 

most satis- 

factory hold- 

era for tents 

at ovor 000" 

0., us they 

combine a 

fairly high 

t o n H i 1 e 

strength with 

frcedomfrom 

scaling. Of 

tho two steels 

tho former 

scales very 

little, while 

tho latter, 

although it 

scales a little more, has a slightly higher 

tensile strength at high temperatures. 

Uniformity of speed in loading is an im- 
portant condition for Htrietly comparable 
'csults. As tho speed of loading increases 
larger strength values aro obtained, Lo 
^hatolior found that with hard-drawn copper 
vivo tested at 250 C., tho ultimate breaking 




KLASTIO CONSTANTS 



iiimiuHiid from 11-4 di 2l-(\ tons por 
ioh as tlio duration of tlio k'Ht decreased 
from 1800 Hoi.'ondN to 20 KL-eonds. Both he 
Cliati'lier find Strilioi;]; lnivn shown that tlic 
elongation of <!oppm p diminishes with reduction 
in (.he speed of loading. 

(llfi) Tl'liMl'KllATlIltr, JillASUIlKMKNT VOIE 
RTKKNOTII 'I'l'iMT.s. With liquid bathumiflieiiml. 
accuracy can iiHiially "be ohltunoil liy tuliing tho 
temperature of the liipiiil, luit it in essential 
that Uui lest should not bo earned nut until 
uniformity of (.omiioraturo id attained. 

With mi air-bath Ihtiro JH incomplete eondim- 
tion of tin! lieal between the, surrounding air 
and tho test |il(!o, and it i.4 neccHsury tlitit tin; 
tom|)oi'ttUirof UinHiini])lo hoiliivelly moafliiroii. 
Thin is moat convi'iiionUy tiJirridd out by moun.H 
of a tliurmo-olcobrio jiyroinotor, wliicli oiin 
oitlior ho ]ti!od in a, juilo drilksd divn tlio 
tost piouo, an WHH dono liy 3iruj;owBlcy nmt 
iS|H'inj!,' or laid (shiso aj-ainst tlio mtinplo and 
bimnd to it with nslmslns Htriiiff. 

Tlio tliormo-isloctric ]>yroinclOL 1 ooiiHisla t>f 
thrt'o distinct \mvla, vi/. : 

(i,) Tho thorino-ijoujilfs a wliioli ruooivcs Iho 



(ii.) 'J'liii iiuliualoi 1 Irani wliich tli tctupora- 
tunjs arc uliactrvod. 

(iii.) Luads (soiinooting Mm tliormo-fioupltj to 
tlio indicator. 

Tlio tlicmmi-iionpki (!oHint of t'\vn wires, A 

Tho (DH|H of 



and .!.!, of dilTiironl, 


composition. 


A and Jtaro joined 




together and form 




t 


a circuit. One 






junction is plneed 


n > 


\ 


in u known tem- 






perature, iiHiially 


c 


. * 


zero, while tho 


* 


. 


other is placed 







agui tin t tho 


\ 




material whoso 






loniporatnro i to 


^ 




1)0 afieortaitiod, 


| 


c 


Tlio dilTweneo in 


| 




tompoi'atni'o bo- 


^ 




tween thewo oiida 


5; 




setHiipan oleetro- 


| 


!/ 


moti vo fm'oo 


1* 


? 


which is |)i'o|)in'- 


| 




tional to tlio tout- 


^ 




poratnro dill'er- 


iS5^_ 




oncc, TliiHlO.lM.li'. 
ia niciisiifed and. 




_L 



thm-mos fbiHlv is 11 oniiviMiimil rracpluclu for 
llie ieo and enl.l junction, 

Vaiioiifi coiiihinatioiiH of nietnln aro UKUcI for 

ti'inpemtiH'fi for wlik'k they urn (n lio used ; 
(n) ISaao metal llierino-cimple.s. 
Iron-eoiiiifantaii (wires} tlun'inn-coiiplos for 



(o(>OO u C. .Imn- 
coii H t a n t a n 
(rods) tlionmi- 
ciouplcs for tt'tn- 
jjni'iifiircii up lo 
K0() T. 

(?>) .Hiiro inctnl 
tioiiplcfi. 

I'tatin inn 
lilfitiiinin mill 10 
per i!i-nt I'liod- 
iinn for tcni- 
) to 




j-mii >.;. FIH _ 

IMaliiinin 
platinum and 10 por cent indium for tempom- 
tmvH n]) to MOO" 0. 

It in cHaiiiilial for loinpiutiii'c;s aliovo 800 0. 
that HID cmipln xlionlil he. ]iri)Lccted Ity (|niii'l'/. 
or porcelain tnliiiH. A thunnn-isniiplis platiod 
in small porcelain tulmij; is ticim at I 1 ' </ r '('y. 

Tho iiiflioiiliii' in nmially n Hi)iinit.ivn moviiiji 
coil galvunomoU-'i 1 of kigk ialoninl oUiulniiiil 




by inoana of a 

calibration, 

tlio 

Tho cold junction in usually placed in ico 

in order to oiifiiiro a oiinstinit loinjicrufciira. A 

1 "liffnot of TllHh F rft]ii])i>mlitirrB on Llio I'ltyslcnl 
I'roportUsa of mnnn Alloyn," I jiimiittianal Asuiciatiott- 
for '.1'rntiitti Mittr.rittls, I Dili, vll,/l. 

* Sou " Tliprimw-miiilpa," (2). 



T~ 

i. 


i 


j 


i 


1 & 


6 


^ 




If 


1 


I.I 




I 


1 



Via, l!ty. 

resittliuioo, having llio sdiilo niarfcfitl in toni- 
poraturo rcadinga which ilppmul ujion tlio 
typo of Ihonno-emiplo otnploycd. Tt in Roiiisr- 
nlly an advantage to iilHn hnvo flio Enntni- 
niont iiniviflcd with it Huide giving its rcndin^H 
in millivolts. 



ELASTIC CONSTANTS 



Complete tlimiio-electric pyrometer ontfita 
ure supplied liy various linns of inntnunisnt- 
makeiy. /%. I3K shows this typo "f indicator 
ivhieh iho (in (hor luts found moat suitable fur 
ordinary high tompemturo test work. It is 
supplied by tlio Cambridge & Paul Instni- 
iiicnl; Company. 

ij(lK>) .DKTMRMINATJOfl OF El.ASTIO Ll.UIT 
AND YlHM) .POLNT AT HlllH TUMPnilATUllli. 
In tlio niiijrn'ity of high iomporatnrc furnaces 
t!u: test, piece is not visible during tho test, 
so that tlio yield point, if (inn oxisfs, cannot 
bn obtained hy noting tho extension by a 
pair of dividers, and tlio attachment of an 




oxtonsmneter is mom difficult than with testa 
at ait- tcmporuturo. 

In 181)0, Martens J a<la])ted his uiii'ror ox- 
tonsomotor for high tniniicmturo work. The 
t(^.st piece /( (l''i!/- 13',) (A)) was turned down in 
the tiontm at cd. Tlio oxietisoinctor cli])9 wore 
attauhcd at li on tho lower enlarged end, and 
wore carded out of the funmco fur attachment 
of tho measuring rhombs at a, Tho extension 
waH therefore measured on the length nl>, and 
coiTontion ivns made for llio oxtcnsioii <if tho 
enlarged ond.s in order Lo obtain tho cxtonsioii 
of tho gauge length r,t1. 

'''iddloff, 2 in J8!). 1 ], slightly modified Martens' 

(/. J\al. Techn. VtrmchmnKlnlien mllcrl'tn, 
.81)5, i)l>, 20 mill 198. 



arrangement, and used two paira of clips, m and 
n (Fig, K!0 (11)), with the mirror rhombs /) 
bo t ween them. IFero again thw true elonga- 
tion has to be nliLiiinod by calculation ; tho 
length o tho thick (iart, however, is small, 
and ag tho whole of tho measured length is in 



The~Z\ro ofjjia Culuos (l 
ISO'C!& 28B 0. hits boau rnlsstl 




Stress in Tons per sq.ln. 
1'IU, 141. 

the furnace, tho observations are unmlliieiiccd 
by variations of temperature. 

Leo and Crowthor, 11 in 10M, adapted lludo- 
lolt'a arrangement of oli]>9 to a horixontal 
testing inachino ; they, however, attached them 
to tho reduced part of tho tent pieeo. 

In Figs, 130 (C) and 140 is shown tho high 
tomporaturo extensometer which is proving 
very useful at tho National Physical J.ahora- 




; 4 C D 10 12 14 10 li! 20 

Stress iii Toiia por HI/. !>> 



tory. This is a combination of the host 
features of both UudelofT and Leo's oxtcnao 
motci'H, with tho addition of two micrometora 
for measuring extensions boyond tho olastio 
limit. Tho olips iia and lilt arc attached to 
tho reduced part of tho test piueo by springs 
and protnido from tho fnniaoe. Tho inner 
clips an are guided on flats on Iho test pieco 
holders by small rollers c. Mirrors and 

3 Kngineeting, IIH'I, xcvlll. J87. 



ELASTIC CONSTANTS 



21 f* 



1'litiinhn aro placed hotwoen tho dips, and the 
whale in (slumped together by a Hpcehd s;priiiy 
attached LD notoluf's on the outer din. 

.Kxtoiifiinn of tho tost piece eiuiM?;i rolativo 
movement bolwcon tho clips an and fib, and 
therefore rotation of tlio mirror rhombs pp, 
\vliic;h IH niensiircrl in tlio umial way by a telo- 
(jopo and swilc. The relative Tiioveinont of tlio 
clips in Jiltm measured by two miuromolura f.c 
attached to Mm inner dips mid worliing against 
tho ontor mica. 

Curves for touts on phosphor bronxo with 
thin instrument arc HUOWII in Fiyn. Ill find 1.12. 
,/'';V/. I'll givea tho eln.stie lino and limit ofpro- 
pnrlionalily at tompitniUirea of 20, 120, and 
2H8 Q CJ., plotted fi'oni rosults with tho rhombs 
find mirrors, and i''iij. l-\'2 nhoww tho full stress 
strniu initvca jvt temperatures of 20, 120, 20fi, 
ii ml 2SH" 0., obtmnod liy using tlio micro- 
motim 

VII. BlJHULTS Ob' TG8T8 AT VAUYINO 



(117) Hi-;sui;rs OF Tiwsius TI-JSTH. (i.) 
Iron and (Jurlwii SlcpJa. Btrongth ti-'Hta at 
high toniiiorftLnros luivo boon nari'iod ontHineo 
tlio oarly iiurt of tho ninoluonlh oisiitury. 

In 1820 '.rroniory and Pniiricr-SainlvlJrico 1 
showed thai, alLhongh tho toimilo Htron^th of 
haiiiincrcd wrought iron \vna 27'(t Ions por 
sq. Btioli nt itir tcniiiomturo, it foil to fi-0 tons 
])or Hq. inoh at rod brat. .Irttirhtvirn, in 1850, a 
fthowod tlnit iron POHHOHHI^ n inaxinnnu resist- 
ainso to fruutiu't) at 2fiO" C!. and this baa 
frequently IKUMI voriiicil for iron and wtool. It 
hfis H!HO liiion aliDwii Llmt this maximum 
ifi jinjurdisd l>y a minimum, which 
alj ubimt 120 (!. 

An oxltaiHivo Korio.H of Uisls wuro oai'i'tod out 
on iron and Htol at tho VVatortown Ai-Honal a 
in IKtJS, from whiuli tho following conclusions 
can bo drawn : 

(1) Tlio chaiigo in (ho ultimaio strong III ia 
very Hnmll up ti> almiit 150 (). Thora ia 
ovidonoH ttf a Mlight rodmstion at from 100 to 
] 20 (!., and u-ftor lfiO (!. Ihoro IH un inorotiHo 
until, at 2fiO" (J., a inaximuin in vi L aolu;d, which 
in from 11) tn 1/5 jior cent higlidr tlimi tho 
mii'iniil. Frinn 2fi() to OfiO ('. thorn ia a 
tiontiuuoiiH fall in strpii^tli, ivliidi at tho latter 
tompomtUTo K' Vi!rt "- reduction in HtrcngUi of 
HO tti Hfi per cunt of tho nnnnal. 

(2) Tlio diistin limit dcni'Ojisiw with inorcas- 
iiif- -trmporaturo. Up to ,150" 0, HUN dcjcronso 
IB directly iiro])orti(inal to incrcnso in torn- 
jjurn.tui'0, no that nt l)fi() (.', tho olastio limit is 
alioiit 70 to 75 pot conL of tluit at normal 
ioni|)onituro. 

(3) With mint iron tho ultiinato Htrnn^th ia 
appi'oxiniJLtoly eountant up to f)00C., after 

1 Aimalcs df.it Mines, II. filll. 
" Ilf/wrt aflhe Jiritith. AmHiiatiiM, 18ri(), p. -ins. 
' Jfllmsim's Malvrvilx of (Jumtrttction. 11)18 edition. 
p. 751). 



whk'li it falln until, nfc (}() ('., it in about 20 |i(.-i- 
tout of th(! inirnuil valuo. 

AliirttiiiH,' 1 in INOO, ])iillisht!d .im olaburatd 
SWKSN of U'Hlfi on tlio stronytli of alcel nt 
toiniioiiitiin.'.-! up to (!(!()"(!,, and included n 
dolorniimitioii uf tlin iirnit of j>ni[Mii'ti(HiaJity. 
Ho iiH'-ril a Mimvllin hiith for teiuticrnturos up 
to 200" O. f a huth of load and tin for tempetu- 
tinxw ii]) tu CtW'('., and for Low tcnipomlnn>n 
a inixtui'u nf thron jmrts by wciyiit of i{? and. 
out! part "E Hiilt. 'J.'oni)>onitiin;3 up to 400 (J. 
wcro inoii&ni'cd with a murourml tlicrmoniitlci 1 , 
and for higher IciinNonilurcH an air Ihornm- 
molor was employed. 

Tests liy .Uio nncl Oruwthec allow that tho 
modulus of olasticity o miliL stool varies from 
20-0 x 10 Ibs. per square inch at norniid. 
torn pcra turc to 12-8x10 at (100 0. They 
also found that the ultimata straws wns a, 
miixiinuni at 250 C., Imt that tlio s tress 
obtained by dividing tho brciildng-lond by lh 
area at fracturo wag a minimum ivt that tem- 
perature. Tho figures given in Tablo 40 Imvo 
been tnkoii from tlio plotted 



TESTS OM 



.K 40 

.STKKI* AT V,IUYINO 



Teinprr.1- 
tnro.'C, 


Mwluliis uf 
Itlaittelty. 
l,ln./a ( |, In, 


Ylclil Bti-fn. 
Ton./H.i. In. 


DlLtiiinto 

Btu-sa, 
Tinis/fS'l. III. 


lli'ihu:lUnl 
uf Arm. 
I'l'i-fi'iit. 


20 


ao-cxio" 


214 


2H-7 


r7 


no 


aiMixio" 


I ft 4 


20-2 


t t 


aio 


28-3 x II)' 1 


lfl-0 


30-0 


(ir> 


,'MO 


27-0 x 10' 


lll-S 


:-t7-o 


02 


1'ifi 


23-3x10 


1B-1 


2fi-7 


32 


fi20 


17-7 xlO' 1 


12-fi 


17-3 


IS 


C70 


M-8xlO' 


0-7 


12-1 


i 


6UO 


12-8x10 










(ii.) Alloy Steels. Tho behaviour of special 
nlloy steolH at high tonineritturo lia-s boon studied 
by Aitchison. 6 A nyndpats of rcsiilla of tonsilo 
U'stts, most of whiuli wuro mndo at thti National 
1'hysicnl Laboratory, ia given in Tablo 41 ; 
these show tlml tho iungeton Btcola with hifili 
pcriiontagcs of earbim (i.ft. about O'ii pur cant) 
hfcvo tho graitoat teiwilo Btrcngth nt lii^h 
tnmpoi'rtlnrcs. Tliiaalronjgth m iicurly equalled 
by tho high chromium H(ccl aluo oontaining 
a high porooatngc of carbon, 

With high chromium ami liidi tungsten 
Btcnla the "[icrcontayo of onrhoii hcnnia tn play 
tin important part in their Htrength (it lii^h 
f.utupcraturcs, TluiH with thci 11 jier cont 
diromiuni ntcol, retlnoing tho oarbon ceinltiiit 
from 1-0 to 0-4 por cent reduces tho toiii!o 
strength a-t 000 O. from 7-0 to 4-8 rona .per 
flquaro ineli, wliilo a roduotion of tlio oliniiniuiu 
content from 11 por cimfc to 0-3 por oont, with 
Milt. a. ti. !!(/!. '/'ccflu, Versurfisattstallm en He rl in, 



1800, 



Vnlvo 
' 



and Vulvo Rtcnh In Iiitrrinil 
/iisl. /lido. Ji'iiy, I'roc., 11)111, 



210 



ELASTIC CONSTANTS 



tins eo-i'lmn content at I per cent, has no odeul 
on tlm tensile Htrenjitli at tluit temperature. 

Wlion llici ti'inpei'aLiire execuds u'()0 (J. tin; 
strength of alloy stools falls oil' rapidly; this 
is partiimlarly notiueufjle witli nickel chrome 



on hard-drawn copper and hrunxc.; 
Hint hi'tmseii -20(J. am! -MiO ;i ( 
1 (.!, corresponds to a decreases nf 4D 
of tho breaking-load nnd an i n oi * 
per cent in the total extension at 1 i~>' 



H '"' lir 



TAB i. E 41 





Ultimate Strength In Tons JUT S<[. In. uL 'LVn 




35. 


(150. 


700. 


750. 


800, 


8r,o. 


1 7 |)i-r ci-nL tiiugsteii, 0-G5 jitirecsiit I'nrlion 


58 


25 


17-7 


13 


10-3 


11-1 


I'' ,. . 0-(5 


15 




J5-5 








M ,, 0-70 


51 


20 


15-1) 


10 


7-0 


10-0 


J2 ,, 0-15 


48 




1-1-7 




7-1 


9-0 i 


11 ,, eliHjiiiium, 0-10 * 


<J3 


M 


12-1 


y 


G'ti 




11 ,, chromium, 1-0 ,, 


67 




15-1 


10 


8-5 


!)-0 


*i' ;l .. ,. 0-5 


CO 




17-0 








'''' >i >P J-l ,, ,. 


78 




18-ii 








:i nioltfl, 0-:i 


fiO 




a-4 








:t .. ,, o-u 






11-5 








i ,, chromium, 0-3i> 






8-5 








:i ., 0-7 ,. 


.. 




11-7 








Ordinary niukol chromium .... 


55 


10 


10-5 


8 


7-0 


5-1 



! 


Hit IH'lt " l ; . 


SH' 




Hfill, 


H 


H 


!!(! 


7 


tl 




if- 


H 


-Ml 


'7- 


f* 


(1-fi 


7- 


(> 




t- 


JT> 




^(* 


*J 




1 - 


L 


:.-o 



iiiul iiiciltol Htcule, lioUvocii vfhinh Uicro 
is vory littlo difteronco at high tomporatun?. 

(iii.) Alloys. -Tho HBO of littings tnulor sii])or- 
hoatad sliOim involvos tin[)craturcs u)> to 
'100 G., mid tho BLudy of bnissus, bron/iis, etc., 
up to Uicao Loiii|iomtnroa liaa been inidoi'takcn 
by ninnisroiis invealigators. Umvin, 1 in 188!), 
coinmiuiloatod a reporb to tho JSritish Associa- 
tion on tt'nsila tests of della inotul, gunniotal, 
inunt'/, niotfil, rapper, bniH-j, phoaphnr bnnwio, 
unit ahiininiuin brono at toinjioraturos up to 
MO 0. 

Brcgrnvflky and Spring, 3 Dow- 
/ 1 and Law 6 hnvo a\nn can-ioil out a 
tlciil of woi-k on this Hiit)jot, 

T\\o linisilo fllronglh (it hih toinporalnrtis of 
aliiHiiiuinn ei>p]ior, aluminium copper inan- 
ganosn, and aliiminhnn '/.inc. nlloyH aro givon in 
tho roports of tlm Alloy Roseard'i (.'ommilteo. 

The variations, with tcmporutnro, in tlic 
liroiioi-fcics of alloys uro fairly regular ; thorn 
is iv fall in tho tensile strong til as tho tompora- 
Uiro rises, with change of curvuturo and 
sometimus humps in tho tcnipoiuturo-ultiniato 
stress ciii-vo. liollcd monol mofcfil, an tilloy of 
70.]jor cent nickel with 80 ]>or cont coppor, 
oxliihita high stnmgth and ductility at tera- 
pnratnrca np to fiflO C, 

Tests at tho .National Physical Laboratory T 

1 Itepurt of Uril. Assae., ISfli). 
1 filter: Atixaii. 'Pest. Mai. Troe., 10(10, vl./l 
J " liltVdt of lllgii TcmpnnitiiiVH mi tint Pliysiral 
iDiMsrtiyH i>f Miimi AllriyH," Inti-rnatinnnl Association 
tin- Tfiihiiy Matmiiln, 1012. vil./l 
1 ''ml. nfMe.tttl#J., lill.f. 

f ami Hlpff /nst. ,/ Jlny 11)18. 

'lrr/i. Kna, 1'ror., SHi llr;ii(ii-(i, 1(107, p. fi7 : 
.ION), i). 11!); lOt.h ll ( .]i () fb, 1012, April 
" fipiirr WIro," Collected 



is alwo a sliylit altoration oF tho in* : I uPmt of 
t'lasticity with tcmpcratnivs nu-t AvilK undi-r 
cliniatio eonditioiiH. 
(118) TJWSILK TESTS AT Low '['I-:M ri;i[,\- 



;ax i-fi:i 
11- 



-TlicHo teats ai'o n.siiiil|y 
by surrounding tho tent piceo" v.-H 
containing a (sooling subHtaneo, aiioli 

Ice for teiniiernturcs down to . . . !)"('. 

loo nnd fa-ox iiiy suit for li.-jnnnratnrcH \ , 

down to t "" -" I ' 

Froxcn meronry for tomnu'riitinradowii i-o - ']()'(). 
Solid ciirbon dioxido powder for tornpom- "X 

lures down to f ~~ HO"C. 

Liquid nir for tumjicnititres down t , - J H5" (.!, 

It is essential that tho Imtli fthoultl 1 u? MIIJ-- 
roinuhxl with H casing containing <]i\%-ti punk- 
ing or asbestos fluff in urdor t> cli(jijn a 
uniform tempmutitro, 

itudoloir, in 1805, found that ir. .n t\iu\ ulccl 
gavo increased yield Htross and uK.i ni itt i-, Mtiocn 
as tho tonipcratiu'o wo- a lownrei], -\vKMn llm 
extension was generally decreased l>v" cfimlinj!, 
Teats niailo at \Vatortown Araeini.1 ** |.^ivi* ii 
inoreaac of about 50 ]>or cont in tin* yield 
stress and 35 per cont in tho iiltmni,t.<* M'IITI-JI 
over tho normal values, M'licn tcalnil t\,t - 
C., but tho extension decreased by <i:j pfi- 

Cftst aluminium light alloys Hhd\v it. 
oroaso over the normal in nkinmio l-i- 
of 9 per cent Jit -80 C., and 27 ijov ,, 
-]85C. 

(110) NOTOIIKD BAB TESTS AU- 

with steel, the work absorbed in tlto 

of a notched bar test piece rises apt fcl lt) 

" /I'jif/)-. 7ecc., llv. ftfj. 
* /((*-. A.ISOI-. Ti-sl. Mat, J'rof.., 



( |, al: 



ELASTIC) CONSTANTS 



217 



fmi'iituro in JnunwHoil ami rrmilio.H it maximum 
ill. about lfj()"('. ; it I hen deeivuweji inul patten 
through a minimum hntwcen '100" (). and 
fiOO" (!., mid riHrs iijrnin iuil.il red heat in 
I'catsliiul. 

Thin work WUH confirmed by <!uil](!t and 

'Knvillon, 1 \\'\\i) nvn (In) li']ii|H:i'atnr(>:! of 

iniiximimi tind niiiiinnnn reftiwtamie to shock 

a.4 *><IO"<J. imd '17.1" (!. 'l']i<>y nay that Minn! 

in no particular fragility in n .steel broken at 

Mu heat pun (.i) ;t^r." (''.). 

(Juillot untl Hnvillon curried out their (culti 
on a llnillnrv (II) Kj^.M. mitehino (sen (100)). 
Tim lent pieeeu were healed in an eiech'm 
fiirmusn In nightly ubn\'i' Urn leniprrjifim' 
required fin' the test, they WITO then placed 
on (lio anvil anil the temporal, nro nnl.cd at llin 
liiiio nf fnuilnro. Tim (.fiiiijinralurn wim clol.cr- 
iniiuiil hy (,ho nun (if n ilii^i'iiii}-i'ou|)ln ttifiorli'd 
in a Mimll hole drilli'd in Mm Miurimcn anil 
]i(ni(it)'at.injj; up to iiliotit II nun. frnni llin CI'D.IH- 
Htiotiuii to In;' frmilurrd. 

Thn ttuth of |,lm toil- |it!C!0 wen? covered will) 
imlujHtoH LD prevail, thd <!<iolinjf of tho ex- 
tmniilioM wlien in (tmitmsb wit.li tlio anvil. 
'IVhls ill as tiliwn l.n HHI"{!, im ]ion(iilili! wens 
hy lii'idiiif; in lioilini; \va(<>r. 
im IIIIH wliowii llniL willi nlloy utonln 
tho iniinlnid l>at' tcnbi ul Iii^li hnniionitni'i'H nro 
a rofloiil.ioii uf Ilio Ic'imilc fil.n'ii^IJi of Mm iilcnlsi, 
l)diii|.; morn or ])w:< invnmcly |U'i)|iiirtioniil I, it 
Ihiil, |U'i)|)i^i ),y- In 'ill (iii^i'.i OKI iticclrt ijiivi! 
lii^licr vnliH'K at clnvali'd Idnipd'atiU'iiH than 
tlmy did n inli?]' noriunl ci 



g (Ilill) It.-MJ. IJAItb.NMHH '.PlWl'K .\T V A II VI Nil 

Traii'KiiA'riiHHH. I'Vli.t Huhin IHIH Hliuwn Hint 
(lie. (siirvcrt (tdiiiicciliiiH liiirilni'SH suiil li'mpitra- 
tuni nir of UKSHIIIIIO tji'iict'iil t'oi'in us tin) li'iisili' 



Aiti'liimni " j!i\''.i ri'Hiiltif of ImrtliH-HM 'c.ttn ;it' 
Htcicln of vnriouw 
fniin 10 jicr cent. l.n 
US ].n]' cent liin^Hlcii, ninl fi'iini 0-li pisr i-nnt, 
(o 0-7 }'\' cent nirliiin. Until iiivi'MtijiHlm-H 
lind a Hiniilar I'l'j-nlai 'ho|i in 1 1m liiirilni'fii an 
tin; Iciiijicnilui'o iiHtrcii.scM. 

In (HH) it ifi jioinlcil out tliut IL tlynuniid 
lianhicHft ti'iil in ^^truini'ly iiBisfitl for tc.stM ufc 
lii^li Inniiu'i'altiri'H, Ailt'luHon ninlcM Hint liin 
liai'dncs.'i tcHt.H wci'o mrriitil out by ('. A. 
Kdn !'(|H, HO Hint it if] prnlinhl^ tliut fhr 
iTHiillH \MTI> iiMninctl liy (1m dyiiainii' 
n ml hod dcsisrihcd by JCilwnrtln in llin pnpoi 1 
rend luii'ni'd thn .dml iliitii in of ll 



limln that tho 
Hltsol ivt tho Icuipriratnni of liquid nir 
(-IHfi (!.) in i!<inhhi that j^ivcu itt iionnul 
(cnipcmliin 1 . 

(1~l) Al/rKHNATlN-U M'l'HKHH Tl-lNTH AT 

VAHVIMI TKAiri'HtA'ruiiKH. ----Very liltlo CN- 
periincnlal work ban heen cnrrictl out on I he 
nllVot of lii^h ti'inpinvi'liii'tfH mi I he nlrciif;th nf 
imildi'ials iiiKior iillornti.tiiif; ti|,n^w:i. Uinvin '' 
(tondniMt'd Homo )CM(;I nl, u lrjii|K'nif,iinv nf 

!!()()"(!, iitnd fniiuiE Ihnl- " I hi 1 hot burn M| I 

vai'ial.inim of tttrcnn raHu-i' hctli-r Hum Ilin cnlil 

dlll'S." 



ni) \\.\n TI;HTH AT J',tiw Tii 



YlcM 





lul nl I'M 1 ' <'. 




Chiii'liy 

''"v" 

t 


IIIMniiiln Sh'CJin. 
'I'nint/Mii, In, 


1'ci' riiht, 


Itrdlli lion 
(if ,\i'('ii, 
J'cr I'cnl,. 


IV.; 11 ' 


SHM 


..::) 


(11 


a-io 


fill-! 


'.'.'.'.Si 


II 


-a 








Ui-Mlil!.' 



m ti'Hl;H on tiarhiin nlrcln at low l.oni[)cui- 
ciirriiiil nut nt Urn Natioiiul I'bytiidid 
Liilinratory, urn [M'VHI in 'I'ablo '1^. 

r !V;iln nt tlm low (cinpiirntiii'i'H on vnrioiiH 
aElny iiU'rlH t<bn\v tlial, j;cimi'jilly, Hmi'i> in au 
hln droji in lite ctirf^y ulmin'hcd in 
biitmtt'ii J?^ 1 *!. anil I0'""(!., Init 
Unit; Iml.winin ...11) unil .-()"('. Mm dro]i, if 
miy, is hinnll, nini hi many CIIUCH thui'O in a 
(liHlincl riwci in tlm value, 

1 liiti't. ,'lviiw; 7V,',/. Mat. I'ri'i:, HiiKI, 11I./-1, 



lnid htir Tiii]>iii'(. 'IV'jil, on 
ft:; lix liV-iinii. Hiii'i'lmi'iiK wllli Jii" 
Vn Niilcb, I nitii. ilri'ii, mid 



HII 1 I!. 

()<!( 

(l-Mt 



trstn (iiirrind out hy th^ inilboB' on 

iii.^ a primitive cliuitin of ;!l loini pi-r 

inish, ultiinatu MIITKH nf 4(1 limn JUT 

inch, |iiir will o.vtniiHion Hit \i(\ nndi 



" "Valvn l-'nlliiM'H unil Viilvn S 



Cimiliimlloii MiiHlnuH," luxt, jlut", Kiia. t'nx'.. ID III, 
" KilwiinlH inul WlUki, "A 1-!UV iN.vi'riiliii! (tin 

Ki'slHliuicti Id I'diHstuitltHi of Alrhilrt wlini li^li'd IM- 

luniarl. wldi n 10-inm, .sti-hl Hull," lint. M,-t'ii. Kim. 

,/., Hll. 

1 I nai fiiti/.VIcfl /ii*(. ./., Mill:.. 
6 "Tcullim nf i\hlti'I'Iiil:l of I'uiHlnirtldii," I1IIU 

iidltlnu, )>, ;!Mft, 



218 



ELASTIC CONSTANTS 



per ccul reduction of area at fracture of fi2, 
gave tho results given in Tallin 4lt. 



Ai/ruiiNMTi.vii iSmuss 



of which the inner or central portion (heart- 
wood) is usually tho stronger in mature trees. 

TABU-: -lit 

rs o.v Hi 1 MEL AT 20" (,!. AND 2.W 1 (J. 



JlmiKC of .Stress. 
Toiis/Su. In. 


Alternations 
before Li'i-actnre. 


Tc i n porn til ro. 

0. 


lUiirmrhii. 


Limiting .Himifl) 
of .Sl.re.ss. 
ToiiH/.Hr|. In. 


4-18-2 to -18-2 


2,429,-lflO 


20 


Unbroken 


^ 


-1- 111-2 to - ll).9 


3,200,501) 


H 






-1-20-0 to -20-9 


3,368,.100 








-1-21-7 to -21-7 


1,121,000 


>( 


Broken 


- -1-21 to -21 


-1-23-7 to -2II-7 


3,2<10,000 


H 






-1-24-0 to -2-l-(i 


J,()9(i,900 


< 


.. 


J 


-l-10-fi to -lli-r> 


2,000,000 


2fiO 


Unbroken 


1 


-M7-0 Lo - 17-0 


2,li;>,(>tJO 








-1-17-2 to -17-2 


aia.ojio 







-I-1G-0 l,o -10-0 


-1-18-8 (o -18-8 


38;j,7fi() 


" 


" 





The tests wore iniule in a machine- of thp 
Wohlor typo, tho teat piece running in iin oil- 
bath heated electrically, and show a reduction 
of 20 per cisnt in the limiting range of stress 
by raising tlio tompomtiiro from 20 to 250 C. 
Tlioy vrci-o carried out at a speed of 2000 
alternations per minute. 

Tuats on some rolled aluminium light alloys, 
by tho same method, gave tho results in 
Tablo 41. 



.Kach animal riny itsolE consiHtH of two parts, 
via. tho inner or spring wood und tho outer or 
sunimor wood, of which tho latter is tho denser, 
harder, and stronger, Tho strength of a pieco 
of timber can thoroforo bo roughly gangetl by 
tho proportion of Hiiinniw wood in tho annual 
rings. 

The width of the animal rings indicates tho 
rate of growth of tho troo rapid growth hoing 
shown by ivido rings thoy thoroforo give 



TABLE 44 
ALTUHNATINO Srnuss TESTS ON ROLLED ALUMINIUM ALLOYS AT 20 U. AND 100" 0. 



No. 


UltlnmUi Stress In HUtlci Tout. 
Tons/tSti. In. 


listliniitocL Limiting ItniiRO of Alteriiiitlnu Stress 
in lOitlijue. TOIIH/MIJ. In, 




20" 0. 


IfiO* 0. 


200" C. 


20" C. 


J.W 0. 


A 


21-0 






-1- 6-5 to ~ 6-fi 


-|-fi-fi to -5-fi 


It 


20-0 


21-1 


10-5 


-(-10-fi to -10-5 


-1-7-0 to -7-9 





28-0 


21-fl 


19-8 


-1- 10-2 to -10-2 


-|-fi-0lo -5-0 


I) 


24-3 


214 


10-5 


+ 10-210 -10-2 


-1-8-4 to -84 


E 


22-7 


20 -It 


Ifi-t 


-)- 9-0 to - 9-0 


-1-0-5 to -fl.fi 



Those results show that, whereas tho average 
reduction in static strength by alteration of 
temperature from 20 to 1CO 0. ia about 
17 per cent, tho conuspomling reduction in 
tho fatigue range is about lit) per cent. 

Tho average limiting elastic range (at 20 C.) 
for the five alloys (A to JU) is about 75 por cent 
of tho static ultimate stress, With steel this 
value is of tho order of 00 por cent. 

VIII. TESTS ON MATEBH.!^ OP OOSSTHUOTKIN 

(122) TRSTINO OP TIMRER. Examination 

of tlio cross-section of a sawn log of structural 

timber shows a central pith surrounded by 

""""tmtrm rings which are in turn encircled 

'itor hark. l<!ach ring represents tho 

voar in tho lifo of the tree. 

V roughly divided 

'""' and aapwood, 



useful information as to tho uniformity of 
growth. 'Mho rings arc umially widest at tlio 
centre- and become closer near to the hark. 
Their width and distribution ofton vary in 
different trees of tho samo kind, in various 
parts (if tho samo tree, and in different parts of 
the samo cross-section. 

Timber is usually divided into two clansen 
hardwood and softwood. Tim former is derived 
principally from broad-loavod deciduous trees, 
while tho latter is obtained from evergreen 
conifers (needlo-leavod trees). Exceptions to 
this classification aro yew and long leaf pine, 
which aro hardwoods although coming from 
conifers, while horso- chestnut, poplar and bass- 
wood (brond -leaved trees) are softwoods. 

Timber is used by engineers principally for 
structural purposes, and a knowledge of ita 
behaviour under various conditions nl stress 



ELASTIC! CONSTANTS 



210 



i it in to bo mud in tlio best 



(i.) I)e.n^ilyaii<lftjw-!jit:(trti.i>Il!f. 
<> Unibm 1 is lurgtsly nlToislod by Lli 
of mointuro Unit it contains!, by ila rale (if 
growth, position in ilio treo, uiul piimii it J4 "^ 
summer wood. 

As tlio doiwity in cloudy rdatod to Use 
miieluuiiiial |m)|iorti(!.4 of timbor, its dolor- 
miriiLtiim in of inijiortiiiico, .It is usually 
jiHOoi'lninod by numsuHiig mid willing 
oai'cEulty jiroimrod piuciss which, for [mtfor- 
oritsd, aro mado in tfui form of tsiibua or ])i'isuiB. 
J'f: h, t, and It urn tho thr<! diniunsrioiiH nf tho 
blouk in eoutiitmlmj and \V tu lliu woight in 



tlinn fbo H|)0(ii(i(! gravity ~- \V/(ft x ( x h) 
mid weight jitvr cubic) fcet---\V(//(& x ( x A), 
whom j/ in tlio weight of a cubits fnot f water 
in 11s. (02-J). 

iror comparative; results tlionidisUu'ocoiitoiit 
mimt bo tlio Haiiuij tho dtmnil v y i Llioroftiro 
usmilly cui'riod out mi drioil Hainpk'H. J (1 or this 
purposo tlicy arc tlriutl in nti ovoii at. 1(10" <!. 
until o coiiKtant wtsit^lit, ami tho doiihity vn\- 
onlntod from thin wtujflit in conjunulioti witli 
tho tlinionHioiiH (dry), 

(ii,) Pcir.Kntiiijc. ii/jl/'oi'.rfHi'fl. AH tlio niedi(iiu- 
onl propoi'litiH nf tiinbou ui-o ail'ootcil by tlio 



1- 












so 

SI 


4. 
IB 

13 


-h- + -t -t 4- 
W J2 J3 13 22 23/j 

1: -I- 4 4 + + 

S/y 10 JO t.1 2S Si 


. A 


""""" 


ant ami number of annual ttnye 


r 


, 
fl*7 


~ ~ ---p ' "1 

4. 4- t- 4- .1. ! .L 

10-7 11-2 10-5 10-S S'6 lfi-2 


I- 


t 
//> 


\- ^. H. -i- f i'T 
G'4 S>fl JO-O^IO-4 fl-S $ 33 









the poi'iiOuta^ooE uiniHliiroinoronnoH. A ilotor- 
iniiHition of tlio jiiM-contnjjo uf inoiHturo IB 
ahvayw nnido from uaiili tustt jiiocii, iincl roHiilla 
tli not iiuJudo Him inforniatioii uro 



'i'lio (It)tormiiinliun of llio inoiHtiii'o nontonfc 
in iniuln on jiiiM.^iS <mfc from cacsli nainnln : in 
Iho oliHO of ti'iiHton,sli(!Jir, and (slmivugo leftist, 
tliCHii nni'int of jii(!(iti Hpliti nft' mljatsont to Uio 
fuiliiro. J'Ynm otbor pi<:(ioH a d'wi or onbn in 
lukun from an near to tho jioint of fmi'turo IIH 



, iiti:., aro ivinf-lu^d iiniiH'diatiily tluit 
limy urn out; llioy ar tlion tlriml in an nv^n 
willi fro oironlation, mid Urpt at a cniiHtiiiiL 
loniiKit'iitui't) of 100" 0, until Umy ooiitiii to 
Juno wciiglit by fui'l-hiti' drying- '.I'lmy imi tlinn 
d. 'I'iio intiiHturo containtnl !M ox- 
UH n iiLM-isonliiyw of tin; dry wisif*lit of 
Iho timber, 



w,,- woijjlit ufli!! 1 
liorttontftKO of innmUirt). -; 100 x (w, l! -V', l )-' ; -in jl . 
In oi'diH 1 to biiHttiii tho drying JH'OIIOHH, tlio 
tosit pioiso ifi HoniotinidH t'ut iiitu Hinall inatitli- 
Ktii'ltH or fthnviiij'H boi'tid fnun tho Hiimiilii uwul, 
J thin is ilom>, 12 lioum* <li'yinjj{ in usually 
nufli*iioi\t. DryhiK nt l" (l " 0, will oliniiimto nil 
ox(!O[it about 2 (lor c<mt of tlio nioiiit'iiro, and 
thin cannot bo removal without igniting tho 



H nf houniH ni'it iiHindly ut into HID all 
pieces for n muiHtimi tlotcnniiiation of 



])ic!t)0, in (inlui 1 t(i cxtiniEno tins distribution <>C 
iiHtiii'c tlii'diigliimt thn Million. '-l-h rtssults 

fnun mush a (lottirJiiiniitioii <m vivw.it (it H]inieo 

and iir arc ffivi'ii i Fif}*- l'^'! and M-l. 

(iii,) Kings 'jif.r inc.lt, percent t>f ISapiouml, tmd 

per coiit of timtiHicr Wood. 'L'hcso ctilii 



Variation of nialsttire aaar tlin motion 
Aaaiatjo Ahlature !>&/, 

1?W. 143. 

aro iimially mado nn tho |)ioco out for porc 

of mointuro doltinniniition, A lino, nno inuli 

long, is (Jiuwn on tho on m- section of tho tlif 











f- 

30 


27 SO 32 


f 


W 


4 


4 4 -l- 


4 


-L 


S4% 


25 2-J ^0 


23 


3Q 


28 


i>o ;:> tf 


14 





B" 



Arrangamtfitt mill number of animal rings. 
Section cut Into cubes for uiofstttra (iateriitliintfan 







y 


\ 




4 


4 


4- j 4\ 


H\ 


t 


/a- 3 


M-3 


M-(7 ] I1'S\ 


1<t-0\ 




4 


-1- 


-I- i 4 


,. 


1 
1^ 


r,M 


13-0 


W.rt ] T.^',7 




10-2 


4 


-1- 


-I- ! 4 


4 


-I- 




?; 


Wl_l.'?-_ . 




"'?. J 



Variation of moisture OHVJ- Iho sect/on 
Auaraija Nol.itiifa r?-0 /f, 
FiCt. 1-H. 

in a radial dlnsotion mid paming through ti 
ri!f{i}ii nf avura^d dovolcipiticiLt. 

'.riio width of Humimir wuntl croMfMud by 1-1'it* 
lino in i(htniii(l by SIUUSUIK oft atsmimuliilivrly, 
on a imir of dividers, tho iviilth of tho Biinuui-r 
wood hnmlH for cadi nnnuiil litiKin nunooHftton. 
Tho Imal distniicci botwticin Hut juiintH of ilm 
dividom, in Imiuirt'dthH of tin incli, in (M|iiul d> 
thu purctntugo of tuinmu'i' wimd. 



220 



ELASTIC CONSTANTS 



llio ^number of rings pot- inch is obtained 
by noting the number of aiimiul ring^ crot* ( >d 
by the measured inch. 

Tho percentage of sapivnod is estimated by 
measuring tho amount of tho crowd-sectional 
area in which snpwoorl appears and expressing 
this us a percentage of tlio whole area. 

8(123) .DKVINO TIJIJIKII TKST Pi K <; GS. In 
order to obtain reliable data from tho various 
tests on timber, tlio information is usually 
referred to some standard percentage of 
moisture, It is considered that timber, if 
thoroughly dried, will roalmorb 12 to 15 per 
cent of moisture from the atmosphere. Somo 
ex peri men tors therefore use 12 per cont, but 
the majority adopt 15 por oont as tho standard 
-for comparison. Tests arc usually carried out 
nt percentages of moisture above-, bolow, arid 

Sectional Elevation on XY 
E 



ju 



P J 



usually left, at least in. ] u ,.,, m 

the cnwH-powlional dimension* " ai 

mderubly longer. Before drying 

tho iierecntugc moisture is oil 

pieces cut from each end of (ho .- 

from this information the reduction * "'nijriif, 

which is required by tho kiln drying il1 * inl(1 >' 

to reduce tho sample- to tho lo'wcr 
content is calculated. The drying of *'' lf ' ' 
sample is continued until thy r^dimti'm 
weight is obtained. 

(124) SIKH OF TEST I'IKCKS von 'I't'.w* 
TiMiiivit. Tiiiiber tests aro divide;*! in(-" 1 
olaasea : 

(1) "Scientific" tests of smafl ,vytf'^'>< 
free fj'om knots or othor l>lciiii.s]i*^ tuul 
uniform moiaturo content. 

(2) Tests on full-size members of 




End Elevation 



Section on EF* 



Via. U5. 



nt tho standard, and for this 
purpose it m nuucmny to dry HampJos fn)in 
tho Jiighor to tho lower figure. 
f Two molhuih of drying aro udoptod, viz. 
air drying (or Reasoning) and Win drying, but 
owing to tho long time required for sWessful 
nil 1 drying, kiln drying is usually resorted to 
lor Lest work. 

An oxyori mental hot-air-drying oven or kiln, 
wlnoh has beon successfully used, is shown in 
Mff. MS. Tho samples aro planed on a tray 
A in a oiroular vesnel B wliloh in heated 
uy *v gas humor 0, and a currant of air is 
drivon through tlits vessel by a rotary fan 
I). _ A aoinjiloLo record of tlio tnmjioroturo, 
which iii never allowotl to exceed 80 C., ia 
obtained l>y a rooordor which in placed along- 
side- tho test Humpies. 

Tho loat ])l(Hioa aro nrojwrcd from tho aainjiloa 
tutor drying, and for thin purpose tho latter aro 



if, |i, 



struts, hoaiiiB, oto., which aro not hoiit* ij^oi \wntn 
and contain floiions defects. 

Tests are necessary under both <* mcli ( itmu. 
Largo Hootlona havo tho saino Kbi-mi^Hi |,,,,. 
unit (iron as small 01103 when briUi. tirt* t ,C [J,,, 
flamo proportioiia and similarly frMi fi'i.m 
defects; but under ptactieal coiidil.jc 
found that this law of similarity isi not 
and that tonts on small jiiecoa yivo ^ r it 
fcho fltrcngth of timber in excess of Urn 
of largo pieces. 

(120) TlWSH.B T.KST3 OF TlHTlfJ- 

compi-ohoiisivo investigations in rc^jv 
ntrongtli of thnher include a, dok-nn i r 
its tensile strength as it is of BdoiiLiUc* j 
anco. TJio roaiatanoo of timber to touml 
pamllol to tho grain is greater than tin dor i 
nthorkind of loading. In timber Mruotiiron 
tension momboi-s aro joined at fcholr <^^lfftn 
othor parts of tho atruoturc, and tlio 



Ui. 



to 



h, 



CONSTANTS 



point isi Uio joint- whic.h In smbjer.tud to 

It follows Unit Uio tennilo ulrrngth does nut 
j.jovorn tins Htriitifflli nf thii nieinlii'.r, and Micro- 
Jimi, from a piuulicuil poinl, of view, it in of 
secondary im 



a flomprc'Hsmnotor ( (D-l)) . Tlioso j^ivn mi 
initial porlinn of the oiirvts wliieh in uppnixi- 
itmtely straight, and it in diiatunniry from 



to iilituin Uio innduliiH <if (slustioLLy, JUK! 
isiimproHnivfi Hli'n at t!i limit- of pnipoi'lion- 
ulily. '.l'y|iiit)il I'csultH iiro givoti ill Table -iri. 



Onl; ( Kiitflirtli) . 

Fir ( Itiiiiiiiini) . 
Kpnum (riiriHfiiinin) 
I'll' (I'olaialiiaii) 



Jnrli, 

7 
I) 
IK 



IVl- l'(!ll(.. 


.Limit, (if 


CriiflliliiK 
Stress. 
]-l'H,/,S((. In. 


MlaMtli'ity. 
Llfd./Si|. In. 


lii'avKy. 


IM 


2770 


fillfJO 


0-illlx ID 11 


0-7(1 


1 1 


iiiSJlO 


(i'l 10 


0-H3X I0 rt 


o-j<;t 


M 


(iOSO 


Sfl-lO 


2-(iOx JO* 


0-7.1 


1^ 


3200 


IIIOK 


1 '08 x 1 0' v 


O-lili 


] j 


7200 


(MH) 


a.ixjo> 


0-78 



Tho liomlH and nhoulili(i'H of tiiiihilo tent 
liavi) l.o lio very grcmtly 



oilier witin fuiliini takew [>lae<; t'itlinr liy oliearing 
o[ thi) cnilH uluiijf U) gt'uiu or hy uruHliing of 
tint e>n<ln tusroHH tlin jf ra in. '.I'lio t t y]i of lust 
]_iii)(io udoptoil i uliown in L'-iij, I-NI. TIio 
ni!(itii)ii Id fniil-iir(( in nutiinilly Himill in cioni- 
])iu'inr>n to Uio cinitH. Test |ti(!isH Hiniilnr lo 
Unit ftliown in Uio fiyuri", liiit luiving Uio 



1 

E 



! 1 1 in md m 1 l-2fi int;lit!H inhli;ml of 0-fitM 

Ill-l) HDIllniillUIH UBOll. 
(llill) (loMI'HIWHKJK TKS'I'.H ON TtMltKll, 

sidii touts along tlio fji'ain giv roliablo 




hut 



. 1.17. 



f tli<u|iiali( ; y of 

HHiiiilly inkvu |ilai;n liy fliiiaring alonj; 
imsliiKiil almnt lit) l:n 75" with llto asm, 
by ldiiL;itii<liiia[ HpliUinj^, Tho 
(/''i'y. J47) nw Ktniornlly priHinti 
3x<t:* or ;ix;ix(l". 

.For invcHtifratory work It in imiml to <lctr- 
oU'OHs-Btmiii diagranm with Uio aid of 



fSlllOAIUMU S'l'ltliNOTJI OFTlJYIHl'llt. I'll 

liy iHilinowlodfijorl by nil iiuUioriUi-H 
111 tit jxouurato teats of tlio slicarhig HtrongUi of 

ri's(f;ig Machine 
War KID i>\ ^ 



.muni. 



d3nBi 



1 N- 1 ' '! -.1. ' 

igngijTEiro 



"^J UouWe Hhear 
\ nionu ttm 

rauat (train ,a 



II'HI, MS, 

ro (lifticuilfc to iniila 1 . Two 
luivo Ijnon adopted i 

(1) With Uio lisal piticn in dun bio 
imlimtod in Pig. 1-18. 

.Testing Shaeftles. 



7os t /'/oco 



M 






Plan of T.;Ht Plncc 
Fill. MO. 



() Witli Uio tiniluu 1 u tic lor 
(/''/(/- ^'llt)- 'J'' 1 ^ HK-Hi'id linn 

HUIIUC'.HH hy WtUTCIl. 1 



Avstralittf 101 1, mi " N,H.\V, Jtunlwwiil 'I'l 



222 



ELASTIC CONSTANTS 



The rosisltuioo of various woods to shear 
across tlio grain has been determined by 
Trautwinc, 1 whoso test pieces were cylindrical 
pins -|- in. diameter subjected to double 
shear, 

jj (128) liKNDixo TESTS. Bending teats arc 
probably the commonest for timber, because 
of the great nun of wood for jufters, joints, 
beams, and other parts of structures subjected 
to bending. Lung pieces of fairly large section 
can bo tested without testing machines of big 
proportions. 

Teat pieces are usually rectangular, arc 
supported at the ends, arid loaded cither in 
the- centre or at two points ns indicated in 
Fiffs. 40 and -11 ( (12)). Tlio latter method 
(called four-point loading) is now generally 
preferred, as the maximum bonding moment 
ifi spread over hall of the spun and in not 
limited to the point directly under the applica- 
tion of tho load as it id in tlio central loading 
method. 

A sketch showing tho direction of tho grain 
at tho ond, anil the number of tlio annual 
lings, should accompany each test, as well (is 
an indication of tho position and modo of 
fracture, Tho position nnd character of any 
defects smeh an knots sin mid also bo specially 
' noted, failure may take place by tension, 
compression, or longitudinal shear along tho 
grain. 

1'or the determination of tho limit of pro- 
portionality and coefficient of dastidty it is 
necessary to measure the deflection for known 
increments of the load. Instruments for doing 
this are described in (50). 

The strength factor usually measured ia the 
modulus of rupture or coefficient of bonding 
strength. Although a fictitious value, it is, 
nevertheless, a valuable index of tho quality 
of the timber. 

The various values obtained from tho tost 
data aro calculated in the following way : 

If I' Total load at the limit of proportionality, 
.U Total load at fracture, 
(---Span between tho supports, 
6 --Width of cross-section of tho test piece, 
A Depth of tho- cross-section of the test 

piece, 

(/--Measured deflection at tho limit oE pro- 
portionality, 

(i.) For central loading (deflection measured 
on length = /). 

Greatest shearing stress - 

Stress at tho proportional limit == 

Modulus of rin)tiiro = 

Modulus of elasticity ~- 

(ii.) For four-point ImtHiig (where the distance 

between the loading points-L, and tho 

doflention is measured on length Z L in 

tho section under uniform bonding 

. Journal, clx, loll, 



moment, and ^ is less, than !_,. .11 and 
P aro tho sum of tho two loads at the 
loading points), 

Greatest .shearing stress = Ifli/'lWi.. 
Stress at proportional limit ~. 31'(( L)/26r7 2 . 

Modulus of 
Modulus of el 



Fig. ]0 shows typical load deflection 
diagrams for Christian ia sprueo and Petersburg 




Dofleotloit in Inches on Span of 30 Inches 
miller Uniform Rcixling AJumuut 

FlQ. 1GO. 



fir, while Fig. 151 gives tho load -extension 
diagrams in tension and compression for tho 
same materials. 



MOD 

, iaoo 

u 
:1QOO 

? Don 

, ODD 

I 400 

] 

I 

200 



9 o o o 

6666666 _ _ , 

Extension In MIHImotma on Ooiiflo Lanutli of20"tmn\, 

14 

12 

,10 

3 

; o 
' o 





_Clirlatli(ia 
ArfatQffttif'laottf\!l'i>llt, 

^ als ^'.'^..{?'%.L-'' 



_llplt of ( rmiiprtlannlltu I 

~S IT' 



Comp'osslvo Deformation (an Qmign l.twulli of 2'% In Inohet 
FIG. 151. 

(120) ToumiNKse) TESTS. Toughness is ob- 
tained by moans of n notched bar impact tost 
in which tho energy absorbed by .tho npoeimon 
is measured by tho loss of onorgy in a swing- 
ing tup which breaks tho material by a singlo 
blow, ./>']>/, 168 shows tlio mmmoi' in ivliitili 



ELASTIC CONSTANTS 



223 



an T/,od testing machine) {HOC- (101))) is utilised 
!.o curry out thin tt.'Hl, and tho form of (cat 
pinon is given in 7 (1 iV/, lf>[i. Tlio tnat ])iece is 
nol,(;bod with tho aiinubu- riii^a aa indicated 



Stool Plato to protect 
the Teat I'lace 




*-.\- Striker 

-Swinging Tup 

Clamp 



-Special I'ice 
fixed to 
Izatt Man hints 



.in tho fikotcii, and tlio top (if it, whom tlio tup 
alrikfiH, is pmteelod by a- Hh'isl platts, 

fm-pitt-l ./fi'.tidin'j Teal. In thin lust tho 
(2x2 x.'iO") is supported at tlio 
(MK!H on a H[IIUI nf 2H 
inolii'H. Tho load in 



//io position of 
the Annual rings 




IL llHMHUlH' UJIOIl UlO 

n ub mi<l-H|mii, 

friim ftl ? ii'.i 

inoli. J ( i)r H 



in imiinaned by 

.*'"(///. 1-inoh iiHii'oinontH up 
itulo ( : <] lOirielien, and thiu r o- 
fiCtoi'dropsiiro mado nt 



(if 2 indie;*, until 
failiii'o. Hammers of 
HO, UK), and 2fi() lbn. 
urn IIHOI!. 

Ditflontioiiii "f UK* 
Hpnohmm tuv mensurctl 
j with (sanh drop, and u 

ourvo in drawn (inii- 
of drop and dolliidtinn fiqimrod. 
'aro obtained from a dnip onrve 
ti-acod mi a rovolving drum. 



VW. 



If \V-~wciKlil "t ill" 
J! ^lioi^lit of ilm 
;i<V:fibi'< stroHH ul nlaHlio limit-, 
I).- mitral d<'flo(ition of Hjiooimoii nt 
limit, 
oF s|KMiii)KMi, 



' WJTL/I>Wt B . 



at 



of 
Work to olnallo limit 



g (l.')O) CLIJAVA i(ii,ii' v. "l?or tlio 
U> splitting tho U.S.A. DcpartniRiit of AgrUiiil- 
tnro iiso tho teat ])5ei!B indicated in .f-'ig. lf)4-, 
and oxrireHH iho roNiills in poniuls ]ier imsli 
of width at fracture. 'iVists bavc bmtn cianicd 
nut to determine tho rcftisduiro to flpliftinjf 
nuliully an well ns tangontifdly to tho annuliir 



fastened ta Clrattsltma 
of Tastiny Mac,li!ne 




Test Piece 




! <'***pV' ff 

i/llff O/ "^itV^ 

c/mfft Sfrtfsa ;/" 



\ t . "Fastened to Oros.ilwail 
of Testing 



rin^H, mid tlio rp.HulU (Tabln -1\\) H!UW tlinl, 
niont luinlwoiidrt uplil inoni unnily iil^ng nidisd 
sH tliun alunj; Uuigcntiul mLi'fai;i.'t!, 



Kind tit Tlnilinr. 


P^SKS'^ 


IwnHlli In 
irk i.f Wldlli. 




Biiill.U. 


'L'uiiijiiiiUul. 


Uimlwouils 

AHll . . . 


3 , g 


;IHL 


Elm , 


2117 


^fi7 


Oak . 


370 


M " 


llr . . . 


l.ltt 


UV 


Hemlock . 


108 


Ifil 


Yolldivpino 


155 


17:i 

i:to 



in roliiiod tn toiiHiln 
the Ki'tiin. A high value in ndvantugwiim fin- 
Linibor wliioli IIUH to bo ftisioncd by nuilH or 

BjllltM, t 

(1J!1) HAHDNKSS TKHTH ON '.ruiiiKH. -'Dhti 
bull liardiicHa tout linn hum applied Ln 



(!) Tlui fii'Ht method, inlnplinl by "\Viu-nMi, 1 
tulluwa tlio Jiiincll U'Ht for ]in\t''l - : - 
ball of fixod dmnifttoi 1 in jn-'- 
timber inidor n known load ~ 
stiitotl timo. Tlio linixlnoftH 
lalcd from tho foi'inuln 

TT 
U "A' 

1 Hf.port of the Dejiartmntl *>J * ,. . 

Australia, iOll.oii " -N.H.W, " 



324, 



ELASTIC CONSTANTS 



where 11 --- (ho Jiardnews number, 

I 1 --- the loud in kilogramme!!, 
A -the projected area of the indenta- 
tion (71Y/-/-1). 

WIHTCH iKie-s a ball >[ 20 mm., load of 1000 
kilos, and time of 2 mi mites. He found that 
the hardness, .along tho fibre is considerably 
greater than either parallel or porpcndieiilar 
to the iiiiLiiiltL! 1 rings. 

(2) Tim tiitenml method, largely used in the 
U.S.A., is to press a ball of 0-444 inch 
diameter into tho limber until it has pene- 
trated 0-222 inch. Tho load required is 
taken tis a measure of the hardness, Tho 
tost tool is a stud bar with a hemispherical 
end. This end projects through a hob in 
tho bottom of a cup-shaped washer. When 
tho tool has poiujtratod the timber to tho 
eon-out depth there in binding between the 
Hleel bar, washer, and specimen. Tho load 
at that instant is noletl. 

With the -Lutlwik eono leat Warren 1 used 
the standard 00 cone and a pressure of 400 
kilogrammes applied for one minute. Tho 
depth was monsurcd by an indicator as tho 
tost proceeded, 

(1112) lir,J*r,y'MN<J]'l Off TlMHKIlS TO AltKA- 
aios AND WiSAH.-~Kolat.ivo wc;ar has been 
tested by proving blooka of tho material 2 x 2" 
under a pressure of 2ti Ihs. against 11 table 
covered with fine sandpaper and revolving at 
08 revolutions per mimilo. A bettor method 
was iiHotl by Wan-on, 3 who utilised a sand- 
blast. Tho test piece, 3 x3 x I", was clamped 
against a plalo having a 2^-inoh hob in it, 
niul together with tho plate was rotated about 
its own axis. A jot of superheated sloam 
under a pressure of 43 Ibs. per square inch, 
carrying sand in it, was projected through 
n expanding- noz/.Io on to tho surface of tho 
rotating test piece. Tho wind - blast wore 
away tho wood on tho exposed diameter of 
2- jnohoH, and tlio IOS.H of weight of tho test 
pieeo in two minutes' exposure gave- a measure 
of tho wearing quality of tho wood. Tests 
wero mado 

(ft) Parallel ( tho dircotion of tho fibre. 

(6) Perpendicular to tho direction of tho 
fibre and perpendicular to tho annular rings. 

(<;) Porpondksular to tho dircotion of the 
libro and tangential to tho annular rings, 

Tho results Hhowod that tho wear wns least 
parallel to tho direction of fibre, tho ratio in 
the three directions being ; 6 : c = l i 2-A : 4. 

(I!13) HOTJHNG POWKR, OF NA11,S AND 

(SriKKS IN WOOD. Nails hold in limber by 
virtue of the friction developed between tho 
surface of the null and tho fibres of tho limber, 
An investigation into tho holding power of nails 
and spikes in Australian limber was carried out 

1 MeiMtrt rif H'. Df.iMiftmanl, "f Forest r>t, A'.N.W., 
in, JUI I, on "N.H.\V. Jrai-ilwood Timlter.-i." 

ma. 



by Warren in I9Il,wh<. found that jVu^l m)iM 
liiubfcf.H were BO bard that it wnn nc5(^'^ Hnr - v .' 
first boro a h<jlo sligbtly smaller thai |-i Lll(i llinl 
in order to prevent cither biuskli"^ * ' ' 
nail or Bplitthig of flic timber. Six'- i ' 1<f ' 1 
S.W.G. smooth steel wire typo IU*-* IH w j' ni 
driven lo a dc])th of 3J- inelic'a in M* 1 -' '""y"' 1 ' 
in liolos bored to nVinoh dianiot^"'- ''''."^ 

were willulrawn by pulling in tin.' (e'MliHK 
machino, and tho loads to ]Mill fr*>iii vnvidiia 
dejiths weru noted. Tho results wlici^^^ I ) - Jial ' 
tho hnlding power was appm\mi*.t ""''X ]"' l( " 
jiortional to the depth, as shown in M'ii''l*> !?. 

TABI.K 47 
lloi.DlNQ PowiiTt or NAM.K 



Depth drivoii In rnchca. 



JMwin 



M,'tB 



&->:*! 



For drivIiiH s[)ikes, holes . 

than tlio dianiolor of the spike mast; l><* tl rilled. 
Warren found that $-inoh tii[uai-tn wi-iitiini 
twisted spikoa required ISO per :t'ii t^ inurn 
load to withdraw them than J-iiU'li mjinirn 
or -J-inch eircidar black iron stniigli t H.J ) i Uvu. 

II.att, a oxperimonting with [ U lT ~ in^Ji l<i 
g-ineh square smooth K])ilw.s niid jHtsn-wi'il 
sj likes ]>itoh ^- inch, root dianiotnr * ,'3 ini'li, 
driven in {-J-inoh holes to a depth <>f f> imr]irn, 
found that tho plain spikes had about fifi JUT 
cent of Iho rcsistanco of Iho soroxv*^! <mv^, 
Hatt's results agi'ecd with those of Wtirrcn 
in showing that tho holding io\vor \\nn 
proportional to tho depth. 

(13't) ImiTAiBsoB OP CONDITIONS or-. 1 TDHTJI 
ui'QN RKSUI/IVS. (i.) The ISJfect of J1/**/.v/-im,v 
Tho effect of moisturo on the. Hbron^Mi * >f \vnnd 
has been thoroughly investigated by 'rioiiimni, 1 
and hia results, which aro fully p;iv(i<ii by 
Johnson, show that there in a lurj^n iniiiviDin 
in crushing strength, modulus of obiM(.i*i t^y, nt\(\ 
modulus of rupture with a dtNinniHU'j in (bo 
moisturo content. Tahlo48 gives tho n,|)pro\i- 
mato figures for spruce, ehestiint, am I piiii>. 

(ii.) Effect of Temperature of Tuxtittf/.- -.'J'Jm 
ordinary variations of tomperatui:** '<if UK. 
laboratory (lflC. to 25" 0.) aro not imj it n-|nn(, 
but if greater extremes occur it in Jicl 
that tho tomiioraturo at whidi th l-i-n 
carried out should be controlled. Tow in 
at .Fordno Univoraity show nn itKsronMo. in. \\ H \ 
fltrcngtli of rod oak ties of from !) pnor nnt In 
1.7 per cent by testing thorn at 0" (,\ innd-ml 
of 20 0. 

3 Jlnli. No. 121, Am, }{;/. Kngr. Asm. 
.-> Jtiill. 70, U.S.A. forest Service* 'JLOlMl im.l 
Circular Wo. 108, 1007. *""", unil 

s Materials of Construction, 11)18 ctl,, ]i. :i.i>fi. 



ELASTIC CONSTANTS 



(iii.) Mffcvt uf Hpec.d i>f 7W/w/. Tlmmton l 
found Unit (10 per cent of tho breaking loud 
givon by progreHHJve loading on tho ordinary 
tiling machine would break IJWIIIH if loft 
in plaeo fni' nine nionlliH. Kxporimentliig 
on tho muiio subject, Johnnon a determined 



Material. 



Unslorn 1 
Hjiruco / 

Longlcuf 1 
jiino / 



02 
51) 
SO 



21 



nf Rupture. 



(32 
J4 
47 



that it wan not wnfo to nHsumn that tlio 
jiermanent load wbiith timber would oarry wan 
greater than 50 per eont of tho short time 
nltimato load an ordinarily found by tho 
testing machine. 

It in evident, therefore, that the nillnonco 
of timo must bo allowed for in touting wood, 
AH a I'otmlt of work by Tiomaim, 11 the U..S.A. 
FimiHttSorvioo of Agrionltiiro havoHtandan lined 
Jibro strain in touting, c.f/. : 

PIT, I null. 

Himiliiif! tcHts (in Unilicr uf Hlvnoliirnl HIMI O'OIIO?" 
Himiling (.ewtii en miiall IMNINIH . . . 0-001B" 
,! ,mn,U..| l B .in, 1U.W.I.-NIJ,,.,,,,,,,. 

lion iwinilh-l [o grain, imtnll tent \ ()i(||) , )(r 

iiif! alung llio (-rain .... (HHfiO" 

Tho Htrengtli of wot or green wood IH mneli 
mot-o Boiutitivo Ui ebangeM of npuml than in dry 
wood. A eliango of tho abovo ti|joedn liy fill 
jier cent may ordinarily bo allowed without 
(landing a variation in strength of over % per 
emit. 

Tho modnhiK of ehuilieil.y in bonding WIIH 
found to bo practically (iminiaiit with 

Of ])(!(!{!. 

(lUfi) TiwrtNu ni.'S'i'oNio, Unirn, AND (!) 



and bruilui from ini c)i]j 1 f !iw*r 1 H Hl.atl])iint am 
caso of wnrliin^, (Uimbilily, anil Hti'oti^tb. 
.DiimbilLLy tlojiondu on ronmtaiuiii to 

(a) AlmiHioii or ti.|;l.rilion, 

(f>) Alworption of watm 1 . 

(o) Al tomato fnui/.iut; mid thawing, 

((/) Firo. 

(n) Anlil, 

1 Ufatfritil* of donHlruvlitia, iwirl. II, 

1 Hilil., IOIS lid,, |i, l!(W. 
* Ami: ,s'o(!. 'j'rxl. Hint, I'riw., HUH, vlll. fi.| I. 

vor-. I 



KtoncH tmcl bridfiff am Hiilijrctcd in pvan 
to fionipi't'HHinn, BOinctitnus l.u tnuiavisi'Ht! ttt 
and Hlic'!irinif, but not to loiittion isxcept 
an would bo ctuiMnd by wind prcNsuro or <itli<!!' 
lateral forccsi. .licHidiw ivsiHliinisf! to UH:BO 
tnvncA Mio siKinifid gi;ivity in an iniportaiit 
pix^iorty. For a given atono tho sjiiicsiJic 
gravity and Htninjttli inoroaHo cimciirronUy, 
whilo for Homo |)iii'|)iwiis greater H(al)ilil,y in 
given by higher Hjnn-ilii! gravity. 

\Villi doiLisriilc, a Unowlodgii of ifn clusLio 
const an In and ten.tih; Hln-ngth, of ils ivHiHlaiuro 
to fatigno and permeability to water, arc 
rerimnito for the jinrpoHeit of dewign. 

(i.) Dclfii'initiiilion of fy'.ajlc, (lravlli/.~li\ 
order to deterniiiiis tin; H]>eitifio gravity (in- 
cluding tlio put-en) tho aainplo in dried at 
100" C. until it IH of constant weight, and, 
when cool, coated with a thin film of pjimllin 
wax and weighed in nir and water. 

It W,,--- weight in air, 

and W,,,-- weight in water, 

.tho Etppotllu gravity -W (l /{W n - W u ,). 
A correction for tho libn of parafiin wax nan 
be made if the remits arc reijiiired to a Jiiyh 
degree of aceuracy. 

Tho true npceilie gravity of tho slmio mill- 
Hlanee in oblainerl by grinding tlio dry H(.(HIO 
to a pmvilur ami del.oriuiniiij; tho HpcuKitt 
gravity of the powder with a Hfimdardined 
l.o (Hiiitoliur a|i]iaratim or Hinnlnr furni nf 
Hjii'cilio gravity ii.ppanitiio. , 

Tho porosity <>f ''he, niiiferial can bo obtniticd 
liy making both tho above detormimitiotiH. 

Then if fv-npi:eilie gravity of tlio Httinn 
HiibHtancd, and tho other valui's aro na 
hoforo : 

(\V rt - vV u ,)/Weight of a eubio unit of ivntcr 

- Volnmo of the Hlone-i- pureH- -A. 
W, r /(VVoiglil: of a enbie, unit of water x 8,) 

E-: Volume of tho Ktono Hitlislimoo-U, 
Then tho porosity - (A ~ B)/A. 

(ii.) Ahsmplinti of Wntci; Tho usual inotlirxl 
of obtivining tin) amount of water which stuno, 
hriult, or eoiierotn will alworb in to 
tho Hp(!i!imen in watitr lit ap 
i!l) u (J. after it hiiii beon dried at 100 ft (i, 
cnoled, and weighed. Tho iinniermon JH 
continued for throo dayn, wlnsn tho Hin-faco 
water it* removed and tho material in ro- 
walgliod. Tho inereaHo in weight' divided 
liy tlio original woiglit and multiplied by 100 
give,4 tho purcentago almor])tion. Tho PMHSCHH 
in aoinoUineH haHteiied by eliminating the Long 
poriml of HoakinH and inimormng tho te,it< pio 
in water whieh in slowly rained to boiling- 
point and kept at that tomporatimi for fivu 

llOlll'H. 

A slight inotlifKsiitioii IH stiinofinics inlni- 
(1 imod by weighing tho Hpoeimen in nir (W (l ), 
in \vator jinnictlinUdy after imniormon (\V U .), 
and iilHO in water after three dayu' iiniimrnioii 



226 



ELASTIC CONSTANTS 



(W', D ). Then the absorption in pounds of 
water pur cubic fool of material 



(iii.) Alternate, .Frte.ziiHj and Thawing. Tliia 
lest is made by subjecting tho specimen to a 
temperature of -.10 C. to -20 C. for at 
least fuur hours after it has been thoroughly 
saturated with water. It is usual to apply ton 
alternate freezings and thawings, nncl then 
employ the master test of crushing. 

(iv.) Abrasion ami Attrition. Baiisohingcr 1 
tie- vised an abrasion test for stone which con- 
sisted in pressing n 4-ineh cube of Uio material, 
under pressure of 4 lljs. per squaro incli, 
against an iron pinto rotating at 20 revolutions 
por minute. The test pieces were fixed at a 
radius of 1!U- inches, and tho abrasive- employed 
waa line emery (No. I)) fed on lo tlio plato 
at l.luj into of 2 gniinincs per revolution. 

This test doea not differ greatly fi'otn tlio 
Dorry lest for 1'oad atones. 

Tlio Hand-blast test wan used by Gary fl as 
an additional abrasion teat for stone. Ho 
gave comparative results by the two methods, 
together wilh tho crushing strength; these- are 
given in Table 49, 



is usually accepted as being the criterion of Uio 
mechanical qualities of brittle material. 1 ] sucli 
as stone, briek, ami concrete. 

In carrying out this test the kind of bedding 
employed has a groat influence on the results. 
Umvin ' ban shown that fluidity of the bedding 
produces verlhml splitting of tho test piece 
and a considerable reduction of the crushing 
strength. Tho common pnuitico of putting 
wood or load layers in between tho lest piece 
and the lesling-nmchino compression blocks, 
in order to allow for irregularities in tho surface 
of the specimen and to distribute the pressure 
over that surface, in erroneous. In order to 
obtain piano parallel faces, Unwin's method 
of applying thin layers of plaster of Turin 
has boon used by tho author for a considerable 
number of tests without obtaining any mi- 
satisfactory fractures. 

The iiiformnlinn obtained from tho test is 
the stress at which tho lii-nt nrack appears and 
tho ultimato crushing stress. It is essential 
that tho load should bo applied axinlly, and 
tho compression blocks are usually supplied 
with spherical scatings (sen (12)). 

From the character of tho final breakdown 
and shape of tho fragments it can be dolor- 
mined whether Uio load wan applied eorrcotly, 
; 40 



RESULTS OF AIIRASION TKSTS ON UUILIIIHO STONES n\r KAI 

Area of Kpooimcns used on (Jrindiny 1'ul)l(i = 7-7fi HI(. in. 
Diiimolcr of No/,/!u on iSand-lilnstitij^ JJoviccitaS 1 ;)!) intslics. 







Volunio of Wear in I'ulilr Inclir; 




Kitnl of Siena. 


Uonmrosstvo 
Strength. 




With Hand Illastt. 




Lljs./sifi. In. 


On Crlmllng Tublu. 















.uiiimj^ui.ii 


1'ariillcl to Itlft, 


UllHIllt 


3H.I100 


0-012 


()-(K4 


O-D'T, 


Grniiilo . 


21,3(10 


0-0-11 


0-037 


o-ofia 


Gnciaa 


21,230 


0-070 


o-imii 


0-015 


I'ovjihyi-y. 


17,8-10 


0-0(ifl 


0'0'Hl 


0-03if 


(Jrnywnokii * . . 


Ifi, 780 


o-oa, 1 ! 


().(),-,;} 


0-058 


Sandstone 


0,0-10 


0-1-I4 


0-lfifi 


0-117 


Slivlo . . . 


7,480 


0-2S.1 


0-111 


0-D82 



A ill-list) HiiiulHtono ccnitiduiiiR KHinileil or angular parlltlus of i 



fclsimr, or slatn. 



A " riitllec " teat is used in tho U.S.Ai for 
paving brick, and the eonditions of tint test 
have been atandat'disnd. 3 It consists in placing 
ton Hft-mplos of tho material in a cylinder 
together with an abrasive charge consisting of 
20 east-iron spheres of two si/.es. Tho loss in 
weight is calculated us a percentage of the 
initial weight of tho samples. This lest is 
somewhat similar to the Dovnl Attrition Tost 
or Lovogrovo Rattier Test for road stones. 
(v.) Oi'uahitif/ f J'e,,itn. The crushing Btrongtb 



Cummniiratumti, IB84, x. 
kuiule, x. ISO. 
* .Standard Hnoci fixation for J'avliiR llrlfik of Lhn 
Ainerlcuu Soclnty lor Testing Mutoriala. Serial 



Photographs of broken ccinereto tost pieces, 
showing the shearing angles of '15, which arc 




obtained with tho crushing of brittle- materials, 
aro given in Fig. IDfi. 

* Report of Jirltiuli Association, 1887, 11. e70, 



ELASTIC CONSTANTS 



For geometrically .similar test pieces the 
crushing strength is proportional to the cross- 
scctional nrca. Within tho limits where 
bending occurs, tlie crushing strength becomes 
loss us tho height of (.ho test pieties increase.'!, 
i'or prisms and cylindors of the sumo hciglit 
ami eims-sectional area tho ei-ushing strength 
a([imred is inversely proportional to the 
omstimCoreiieo of tho test piece. 

Tho comproHsivo Hlrength of eoimreto in 
rcdiuied, hy mi excess of water during mixing, 
to n fractional part of that which it would 
ranch under proper conditionH (sue Tahle oO). 

TAIII,!-: fit) 

Kfc'Fi'Ktt 1 or VI-JKOKHTAUK on WATKII ON Tin; 
CHUMMING HTiiiiKivni OP C'oMdiirrn 

(1'rom U.N. Sun-ay Hull., No, H-H.) 





{.'llliurut 


ilsas-lltf 
},\l*,/ 


1 III-. 


Cms 


1 Ills'. 




1 Miiiilli. 


I! .HiMiilm. 


8 


liUUO 


11814 





Hfi.17 


'1BOS 





4(11 ^ 


-I8R1 



mil 
ifii 

12(1 



41)0 



(Jrnnl)ing li'st piinniH of ImiMing BLiino are 
nsiiiilly in HID Tonii o (uiliiiH of -1-intih Hides; 
for (ioiHirote, (!id> of from 7- to lO-imsli fiitlijK 
aro employed ; while liriokn am goiiorully tOHted 
on the Hal;. The diimmsionH of tho k-wt piocsoa 
ami, with hi'ickH, direiiliim of oniHliing are 
H given with tho 



227 



(1110) THM ELASTICJ 
BHIHK, AND CONIMIT;, Tt hns been shown 
that a linear relation is often not olitmued 
hetwcen stress and strain for Ktonc, liriolc, find 
concrto < ((!!}), and that for the latter em- 
pyn'cnl moduli are used for the purpnacs of 
design (mloiihitioii. 

Stiuiton Walker l gives the following par- 
ticiiihu's of the innnniii 1 in which diffci'ont 
vai-iahlcfl affect the strength and uiodiilus of 
clttHticity of conei'eto : 

" {) Eoth tho modulus nf chislicity ant! 
strength increase- within certain limits us tho 
aggregate bocomcH coai'Hor, atthimgli the 
modnlns of elasticity increases less rapidly 
than the strength. 

"(/>) An iiKiroRso in tho quantity of cement 
in tho biilish causes an inerttaso in values of 
modulus of elasticity and strength. Tho 
modulus of elasticity is aft'ooUid aomnwhat less 
hy change in the cement content than tho 
strength. 

" (B) The quantity of mixing water exerts 
a most iinu i l:(?d efi'eet on tho moihihiH of 
clastioity and stnMigth. An atldition of 25 per 
cent of water to a uiixtuns of normal con- 
sistency deoi-ciisca the modulus of elasticity 
ahoiit IT) tu 20 jir-r wnt, antl the strength 
ahout IS") to <H) ]ii:r ciiiil. 

" (if,) .lioth the moduliiH of elastioity and 
strength incronso with the nge of tho (ionorolo 
so long as the Hpiwimmm are kept moist during 
curing. The strength hiiTe-iincs in ])i'oporti(>ii 
to logarithms of the nge. Tho mudnhis of 
ela.ititiity follows a[)])roxiniutoly the mine 
relation. 

" (n) There SH no marked difl'creneis in tho 
modulus of elasticity and .strength of eoncrolo 



Blimc 
(lianiti) 



Briokn 
Vitrillod hridk . 

Common ili'Hln . 

Comnxin 
f.ciccHtor wii'd-uiit 
i''ldtloa 

Whili! ^iiiill, ivlrii-isiit 
AyU'Hford icil ]>rcw(dil 

Lolllloll lll'Hli HllPllkl) 

Common i 



(Jrnshltiit .StvdiH!l 
. Um./Hq. In. 



LY.!<)0 

1, (100.^,8(10 
l.lifiO. 1,1100 



Trims verrto 'IVHt. 




Miiiliilitfi of Jiuptiirt), 
l,liH./H(|. la. 


1'cr (it'll t. 


2710. IHHO 


O-l-l -ft 


11(10-1 (1(10 


*|. ;!-(>-'! 


31HM320 


0-7-S-3 


Over 1100 


lii'SH limit ft 


IKID-OOO 


fi-l'J 


4(11). (1*1(1 


12-m 




tlvor 1H 



Hepresontativo (ii'imhiiig, bonding, and ab- 
sorption results on tttoiui and lu-iok ai'o given 
in Tablo (11. 



made from high-guide nehbhiH, (snishct! litno 
Btuno, erushiid gi'unito, UK blast fumade "lag. 
1 Amer. Woo. Teal. Mitl. I'run., JUIO, (). &!, 



ELASTIC CONSTANTS 



"(/) A comparison of speoiniena stored 14 
clays in dump sand imd 77 days in air with 
specimens stnrcd 01 clays in damp Hand shows 
that the modulus f elasticity and strength are 
higher for the damp sand storage. 

" ((/) Testa for mixing times ranging from 
J to 10 minutes show both tlio modulus of 
olaHticity nml strength to bo greater for tho 
longnr mixing limes." 

(137) TivNsitJi STIIENOTH OF CONOIIKTR. 
Considerable difficulty is experienced in design- 
ing suitable end attachments for lonsilo tests 
on concrete. _ Many experimenters (sa.sk spheri- 
cally headed holts in tlio contra of tho ends 
of tho tent piece and pull on thesn beads by 
tho tc.H ling-machine grips j others enlarge the 
ends so as tn form tlio tost pieee info a flat 
dumb-bell shape. I'artioulars of a few dimen- 
sions which have boon adopted arc given in 
Tivlilo fi2. 

The Icnsilo |,rength of concrete is aliont ono- 
eighth to ono-tonth of tho crushing strength. 



' V(1 
for 



beams for transverse teats. ,, _ 
beams 0" x fi" loaded centrally <M1L IL H| " 1 " 
of 30 inches. The results he ol>t"' llt!cl . "" 
1:2:4 concrete, mixed by vohmio* tt - 1 ' 4 ' f-'' V(1 " 
in Table G,t, 

(140) INCHKASJ.; or S'riii: 
CKETE WITH AOK. Tho avi 
ago of strength of concrete at .,.- 
assuming full strength at one yuu- 
in Table fi4. Thoro is no n>lial.*]< 
strcjigtli of concrete more than ^ 
old. 

(141) ElTECT OF FlllRATION, ,tjfldl N". '^' J 
PwESSUHIi! ON THE S'l'HEWtlTIt OF f ." J W< sit' 1 "! 1 !':.- 
Vibration and jigging methods aro nmofnl for 
getting coneroto into place arouml I't-i nfiu'diriK 
bars and in intricate forms, l>n t ^" l|(1 
good, and in some cases aro f i,-i ruifrilj if 
applied after tho coneroto is propcvrly p'fiirnil 
in ])ositin. 

Aht'iiins. 2 finds that the vihrnl-iom "f "" 
electric hammer has very little iufliuMifici mi 



TAIII.I.; 63 

OF TtmSILH AND COM PItESSION TjJST PlECES FOR 





Authority. 








, 


ITattJ . 






\Vool aim \ 
St. I^oii is 


i . 

; Teafing Laboratory [ 


S"x8 
em 



I'ensllo Test Mora, 



" x3fx 21" prisms. 

" x 18" priFtniB, 

4":<'J" (I bar) 171" gaugo Icngtli. 
mvo orosa-Beotion enlarged c-nds. 
Hqimro section (onlnrgcd 
ends) 5 fcot long. 



. 

G v oubes. 
8" diiimofovx 12" cylin<.lc-i-H. 

fl" x 6" xH" prisms. 

j-'IJ" diftmolor, fil" UPLIU* (c^vJ 



* Assoe. lliigr. fine, Joiirn. sxv. l.jfi. 
t llVst. .Voc. Jifff/. JoiH'ii. is. 234. 

nnJ 1 ?r i:i }, m V, 1 "' oy i 1 !!' 1 ]l( lm ca. " Stniotiirnl-Mntermla 
320, f/.S. 7Jtip(. of Qcolot/iml fittrveif, 1008. 



t Cornell Civil Engineer, xix. 100. 
S Jv'Hffi 1 . AVw'fl, llli. 501. 

Labonitorios lit fit. Louis, Sto.," Jtttltrt.in Ki 



(138) Srriun STHKNCJTII OF CONCJRETE. 
The ahcur strength of concrete lien between 0-4 
mid 0-6 of fche crushing atrongth. Tho shear 
testing (ool is of the asuno form as that used for 
ntotnla ( (1% but is specially arranged to 
tnke a larger teat piece. The tost pieces aro 
genoraEly cast 6 or (I inches in diameter and 
M to IS indies in length, and arc tested in 
cither ainglo or double shear, 

(180) TliANHVKHSBSTKENn'1'ItOpCONOHE'rE. 

No definite ako has been etandardisccl for 
TABLE C3 


tho strength of puddled concrete win*"!* rrppHi'i 
for poi-iods not exceeding 30 acusori^lH. Jf i 
greater time of vibration is employed, UMUXI i: 
a steady falling-o/V in strength. 'Aft-^i- -If. t, 
CO seconds tho strength in only i)D ic.*r cm 

TAIILK fj'l 


AGO. 


l'^:rt'nnl:^!-;*^ <*f "[''nil 
Strmiucf-li. 


7 dayn 
1 month 
2 months 
3 
4 


,, 
12 


;tt) 

fiO 
7fi 

an 
fjo 

95 
93 

lfll> 




1:2:4 Ooncreto ABO 
1 Montli. AvprnRQ of 
25 to 27 'JcsLs. 


Tensile slrcjigtli ILs./ \ 
([.iii. (K,) } 
(.'oniiirrssivti Btrongth "1 
DxH>j, In. (S ( ) / 
Modulus of rupture \ 
Iba/sq. in. (tii) / 


180 
1040 
3,12 


of that given by tlio standard iticMtud of 
puddling. 
J pressure is applied to cniioroto aftci 

1 tlnlvcrslty of WlBconsin, Hulletiti Nn, '1W7 
E "]Sffoot of Vibration. Jiggins, inu] X.rt -Kauri! (in 
Fresh Concrete," Structural ainlorlaJa 'llt^nin' 
Laboratory, Chicago, 1010, Mvtletin Mo. 3. ~ l - KU ' ri -" 


Si=0-lS B .l.-80Si. 



ELASTIC) CONSTANTS 



moulding, water is expelled and a drier concrete 
is produced. This gives increased strength. 

Abmms finds that 
a pressure of from 
200 to fiOO lliH. per 
Hq. ' 




h 




' 




x< 



to equalise the procure. Three gauges (I 
fire provided for reading tho pressure tine on 
the. nir reservoir and two on llm water pipe. 
Readings of Mm water collected in tlio can A 
are taken at fre([iicnt intervals at tho com- 
mencement of tho test; lint the rate of 
percolation of ivalor 
(Ummiiilies as llic test 
proceeds, mid. tin; 
intervals helvveon tlio 
readings fan ho 




reduced until it 



c c c c t< 

(For Test PliiKo oonii/icletl at 
aoo Fig. 157) 



If>0. 



ing increases tlio coinprcwsivo strength by 20 
to ;ti) per cent, 

(142) PMIIMUAHILITY cw CONOIIKTK ANI> 
MOBTAK. Pornieiiliility dojicnds upon ininnto 
pussiigo ways in the inatorial whioli arc HO eon- 
ncotcd that wator (tan flow right tliroiili. 
Tents iimler high honds of water have Imim- 
iniwlo, and sliow that oven coinont paste is not 
absohilply iTii])(n'vi(Hia. (,'oneroto and mortar 
<tati, nevertlwb.is, ho mado wliidli, innlisr 
normal jH'cHSiirun, do not show any dampness 
on tlio oHUmltj. 

Two niolhoils of lest are employed : 

(1) Tho amount of water pawning through 
tho material is collected and weighed. 

(2) Tlio weight of water, whteh has to he 
suppliod in onloi 1 to hoop a oonstiint lieiul, IH 
mouanrod (/., tlio water i;oing into the 
test ]>ieoe). 

Tlio arrangoini!iit of a Hiiitablo apparatus 
for Method 1 in givon in ./ ( 'iV/. lfi(J, and a 
flotition of the tent pieee, together with tlio 
can for oaLi'hing tho water, in Fig. I'fi7. 

The test jiiei-o (? imtliea diametor) lian 
annular HpiuscH at the outer edges of both the 
In]) and liol.toni mu-faee [lainted with a rubber 
waterproofing piiint. Tlii leaves an annular 
]>ieee fi inrthen diameter in the original con- 
dition. Kuhher wanlu'H A, A are placed, over 
tho iviiterprooling, and tho Hpemmon in seoiiroly 
clamped between the two eaHt-iron plates 1', 1*. 

Tho water IH applied to tlio top of tho tost 
pieise through the pipo (!, and any ivator 
passing through in caught in the ean 1J. Tho 
Hpeeiinen in Hoalted in water for <1H hoiii'H 
iniined lately before the lout. 

Tho arrangement ('Pitj, IfiO) pennitH of MX 
teats being earned out at inioo. J'laeh test 
pioeo with its holder & atlaehed to a union ('!. 
Tho water pannes through a iilter B and 
tank I'] before reaehing the spoeimon. Air 
prcsHiiro IH supplied to the tank 35 by a 
compressor, an air reservoir ])' being inaortcd 



tho waler supplied 
(Method 2), tho 
arrangement in 

slightly modified by fitting a waler reservoir K 
above the teat-pie holder (Fig. IRS). This 
reservoir is only partly full of water, and the 
pressure is applied to the top of the water by 




B- 



iuclios - 



1'iu. 157. 

the compressed air. Tlio amount of water 
added at regular intervals, to keep the level 
constant in tlio gauge glaw II, fa reeonleil. 



230 



ELASTIC) CONSTANTS 



With nn inveHligatioii ciin-iod out at tin 
N.l.Mj, mi the permeability of reinforce* 
concrete under n pressure- of 8-7 Iks, pei 



Y Air Pfcssitra 



Water 
ftosaruolf 

(K) 



Water initial to keep 
lend constant in 
Gauge Glass 




FIG. 1G8. 

square inch, nir pressure was replaced by an 
actual head of water of 20 feet, which was 
kept constant by adding water to a reservoir 
as described for the last experiment. 

(143) TESTING UOAD MATKRIAIVS.- There 
aro two methods of estimating tho comparative 
valuo of materials for road oonstrnction. The 
first is to lay sections of a road with the 
materials which aro to ho compared and observe 
tlio effect of traffic on thorn, and tlio second 
is to subject tlio road materials to laboratory 
tests designed to imitate actual conditions 
mot with on tho road. Tho former method, 
with great care, will give results, but the 
process is long and costly. Tho use of 
some form of experimental road factions is, 
however, tho only thorough method of teat- 
ing asphalt carpets. Observations of tlio 
behaviour of macadam roads, constructed 
with rooks whoso physical characteristics 
have boon determined by laboratory tests, 
enables these tests to bo used in order to 
judge- tho probable adaptability of any 
rock for use in road construction'. 

A determination of tho relative road- 
building qualities of different typos of rock was 
first systematically 'attempted in Franco. Tho 
.(.'Vouch School of .Bridges and Roads installed 
a road materials laboratory in 1878, and it 
was thorn tlmt the Dcval 'Attrition Machine 
was designed, and its excellence has led to 

' Ann. ties jmnls ft o/KiimsA's, IS7D, tnul IMlelln (lit 
Miwettmtlca 2'ravmtx publics, 1881, 



its general adoption 03. a atoml"- 1 "* 1 ll '" lm l! 
ma dh i ne. 

Tho testing of road metal wiis iiiitiu^ 1 '' in 
Germany in .1 884 at the liral; Munitsli *--' >J J f* !n ' tl(>|1 
for .Establishing Uniform Condition n "^ 'IVMing, 
They appointed a committee to <lra-N. tint 
metluKl.s of testing that were IIGC:*-H 
work performed by this cdiimH 
reported to conferences hold in 
and IHH.'t, and definite proposals <>'" ^(""linjfi 
including tho Deval test, were sii lutii t,i<-(l uml 
apjirovcd. 

.in 18i);ti\raHsaolnisotts Highway Ooiti niJHHinn' 1 
founded a laboratory for testing rim* I iriftlcrialii 
in the Lawrence Scientific School of .1 I urvnrd 
University. In 1900 the United Shit**-* ( <<'Vi-ni- 
nient, because of the growing irii (lorlnrKii. 
of road-material investigations estn-I *liHh<itl IL 
laboratory in the JJiirean of ChoiiiKl.r.V' *>f Hut 
Department of Agriculture. This ln.li"oivi.(my, 
traiiHforj-ed in lOO/i to the Offico of 1,'ul'l'i.i 
examines, without chargo, H(i-inf*l'M n( 



ii < 



f I Ins 



, 

oad material submitted by aiiv'eitiKt' 
United Slates. 

'i'lto only stone-testing a])liiuu!* lnOii-vn] 
to bo in existence in England prior in I1M1 
was tho ".Rattler" attrition muftliM"', tli- 
ligned and used by E. J. Lovogr<)v(^ rt J innniijli 
Hngincor and Surveyor of HornsBy. 

In 1911 a road laboratory was' infiiiM 1 "'"!' 1 ^ 
is a division of the Engineering :i:>-pitr-l,ini'iil, 
of tho N.P.L., Ted<lington, in n.ci-i(t<iixlimni 
with a scheme drawn up by tho K*mcl 'Hmml 
uid approved by the Treasury. '.I'lio wtirk 'if 
;ho lioad Board baa now boon tiilcmi tjvrr liv 
thoSlinistry of Transport (Roads .Do [ un' l-riu-iil.j. 
In order to preserve continuity with Mm 
work which has been in progroHM in ulJini- 
ricH, standard types of ' nuutliim-H, JIM 
iscd by the Dnited States oniuti of J'nMio 
ioads, were adopted. 

(M'l) A-ITUITIOW TEST, Tho 
isod for this test in of 
he four - cylinder .'Dcval 
yi>e, whicfi has given sutis- 
iiotory rosnlts in Franco 




FIG 



fiineo 1878. It is shown in Firj. J r(l, H. MI | 
consists esaontially of four cylmiksrw, 71. ; 
in diamotor and 14 in. Jong, inourHHitl nn 



* JlvUelin Wo. -14, on Physical Testing of ft*,rj;- H r,, e 
Boa* ItoilMw, U.K. Dopnrtmcnt of A B ?Ioii1 1 VT- 

3 .Lcivocrove, J-'lutt, and llowo, lioail-mafc inri ffftw* 
Attrition Testa in the lAghl of Petrology. r*tnct. 



ELASTIC CONSTANTS 



231 



a frame in finish a way that their axes aro 
inclined at IJO" to tho axis of rotation. 

Eleven pounds of rook, numbering as nearly 
fifty picocs an possible, aro placed in one of 
the cylinders, tho cover bolted on, and tlio 
machine revolved 10,000 times at a rate of 
about 30 revolutions per minute. Tlio 
dimensions of tho stones should bo such that 
every stone will pass through a 2A-in. ring 
but will fail to pasa through a 2-in. ring. 
Only tho material worn off which will pass a 
stove- of jVin. mesh is considered in determin- 
ing the amount of wear. This amount is 
expressed m a percentage of tho 11 Ibs. used. 
Ju addition (he I'Ycnoh coefficient whwh is in 
general UNO ia oiilonlatci!. This in defined by 
the relation 

lYoneh coefficient of wear -- .;-,- , -. 

J/oreontago of wour 

A wot teat is also made, and for this pur- 
pose 1-1 gallon of wntor is placed with tho 
11 Ibs. of stone. With the majority of stones 
it is found that there is more wear under a 
wot teat than under the dry test, but occasion- 
ally tho revci'HO is tho caao. 

An approximate relation has been established 
botweon tlii.s machine and 1 .ovogrovo's I loniKoy 
"U attic r, 

(Ml>) .KKl'HATKll 'Bl.OW Til TACT {ToUflH- 

NK3S TKHT), (i.) I'mpriftttitni- / H}>;iiiie,ti,~ 
The specimen is prepared in the form of n 
cylinder 1 in. diameter by I in. long. A 
piece of the rook is roughly chiselled to mze 
1|-" x l ; |" x IS". .It IH ground approximately 
eylindrical on a largo eryslolim wheel, and 




in the chuck of 11 grinding machine, 
whore it IH ground by a. small erystokm whtiol 
to oxa(!tly 1 in. i diametor. Tho ohuck mid 
stono aro then taken to tho diamond nmv 
(Fig. 1(10), whoro tlio spoeimon is ouli off 1 in. 
in length. 



(ii.) The, Tcsttiuj Ulnchinc. '.I'lio iiiJicliini: 
iisud foi 1 this totit ia known as tlio I 'a go lni|iiu'-), 
Slanliino (Fj'j/, 101). The blow IH given liy 
a 4-4-lb. liamiuoi' IT, and nets through a 




plunger I 1 whom- Kiirfiuio of oonfnud with tlio 
sjiecimon \ Hiilicrioul, anil hax a mdiiin of (}-<l in. 
Tho blow, aa thim flolivorwl, approximate 
to tlio blown of tmlTto, and tho ajJuirifinl enil 
lias tho furtlior advantngo of not 
grout oxaPtnosa in potting tho two 
Biirfacea of the tost ])i(Hi parallel; tho on tint 
load being applied, at ono point, on tho upper 
Hurfiuio. Tlio teat- connistii of a 04 in. fall 
of tlio hummor for the lii'.st blow, and tin 
inoronHcd fall of 0-1 in. for each ftiKwraling 
blow, until failure of tbo spcninic!!! ot!(nirs. 
Tlio number of blows I'liimii-ccl to destroy 
tho test ]iit!(;o IH lined to repniHMit tho 

ll 11098. 

A sprocket tihain H drivwi from (bo Hhafting 
in supported on H|irooket wlu'ds altaoheil to 
oaafcings at the top and nimr lo the IKIHO of 
tho maohinc. Tlio olinin is provided with 
small lugs whieh engage a Hpi-ing hult attiuih- 
mont projecting inwanls from llio top of tho 
hammer. Thm raiwa the lianunor nni.i! it in 
tripped by a rod R pnjoe|.in downwards f nun 
a orosahcad whioh Hlides on two 



ELASTIC CONSTANTS 



the upper and lower (sastingn. The oross- 
head in mined iLiilomiitii.-rtlly through 0-1 in. 
lifter every blow by a lead sore' driven by a 
worm uml worm-irheul atlrushed to the minio 
shaft as tlic, upper sprocket wheel. 'Ky 
Hi rowing tho lend screw out of gear witli tlio 
orosahead tlio liitior (tan bo raised or lowered 
through iiny dosiriid height or the test can bo 
made wilh a constant height of fall. 

A slightly different method of- preparing 
tlio tost sample is sometimes employed, vi/,. 
by tlio use of u core drill. This coiiMistH of a 
brass core tii Im having at its lower end a 
uleol rimr containing eight small diamonds 
in itH cutting edge, four on tlio outer edge, mid 
foni' on tlio inner edge. Tho drill arranged 
to out a rook core 1 in. diameter nnm at 
201) to Ml) revolutions per minute. Water 
in supplied to tlio inside of tlio drill and the 
specimen, through a. stationary brass ring by 
a rubber Lube foil nee Mi in. 

JJO'M) AHHAHHIM TEST. T.ho Hpeoinion in 
in tlio mine manner as that for tlin 




ropoatcd blow impact tost, and in ensus \vhere 
!)oth teata am iwjiiired the spwiimonH can